Java Math abs() Method

In Java, the abs() method returns the absolute value of a number, ensuring it is always non-negative. Part of the Math class, it supports int, long, float, and double, making it essential for calculations in finance, gaming, and physics. 

Unlike manual checks, Math.abs() offers a cleaner, more efficient way to handle negative values.

This tutorial explores the abs in Java, its syntax, supported data types, practical use cases, and best practices for optimal performance in Java applications.

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Understanding the abs() Method in Java

In Java, the absolute value of a number is its magnitude, meaning negative numbers become positive, while positive numbers remain unchanged.

This function is particularly useful in scenarios where negative values are not meaningful, such as:

• Financial applications (ensuring positive transaction amounts).
• Distance calculations (e.g., computing the difference between two points).
• Game development (ensuring movement calculations remain positive).
• Physics simulations (handling velocity, acceleration, and force calculations).

Unlike manual conditional checks (if-else statements), Math.abs() provides a concise and optimized way to handle absolute values across different data types.

Here’s the general syntax of Math.abs():

Math.abs(value);

Parameter: A numeric value of type int, long, float, or double.

Returns: The absolute (non-negative) value of the given number.

Math.abs Java Example 1: Using abs() with Different Data Types

public class AbsExample {
    public static void main(String[] args) {
        // Integer absolute value
        int absInt = Math.abs(-10);
        System.out.println("Absolute of -10 (int): " + absInt);

        // Long absolute value
        long absLong = Math.abs(-100000L);
        System.out.println("Absolute of -100000 (long): " + absLong);

        // Float absolute value
        float absFloat = Math.abs(-5.5f);
        System.out.println("Absolute of -5.5 (float): " + absFloat);

        // Double absolute value
        double absDouble = Math.abs(-12.34);
        System.out.println("Absolute of -12.34 (double): " + absDouble);
    }
}

Output:

Absolute of -10 (int): 10  
Absolute of -100000 (long): 100000  
Absolute of -5.5 (float): 5.5  
Absolute of -12.34 (double): 12.34

Explanation: Abs in Java converts negative numbers to positive while keeping positive numbers unchanged. It supports multiple data types, ensuring flexibility in handling different numeric values.

Internally, the Math.abs() method performs a simple conditional check:

• If the number is negative, it returns the negation (-value).
• If the number is positive or zero, it returns the value as is.

Math.abs Java Example 2: Understanding Internal Logic of abs()

public class AbsInternalLogic {
    public static int customAbs(int num) {
        return (num < 0) ? -num : num;
    }

    public static void main(String[] args) {
        System.out.println("Custom Absolute of -15: " + customAbs(-15));
        System.out.println("Custom Absolute of 20: " + customAbs(20));
    }
}

Output:

Custom Absolute of -15: 15  
Custom Absolute of 20: 20

Explanation: If the input number is negative, the function returns -num (negating it to make it positive). If the number is already positive, it returns the same value.

Also Read: Exploring the 14 Key Advantages of Java: Why It Remains a Developer's Top Choice in 2025

Now that you understand how the abs() method works, let’s look at the different numeric data types it supports. Knowing which data types work with Math.abs() will help you use it effectively in various scenarios.

Data Types Supported by abs() in Java

Java's Math.abs() method is overloaded to support different numeric data types, ensuring flexibility across various use cases. Whether working with whole numbers (int, long) or decimal values (float, double), abs() consistently returns the absolute (non-negative) value of its input.

The Math.abs() method in Java is overloaded to support multiple primitive numeric data types:

Each version of abs() works the same way: it returns the absolute (non-negative) value of the input number.

int Absolute Value Example

The int version of Math.abs() is used for standard integer calculations where negative numbers need to be converted to positive values. 

Math.abs Java Example: Using abs() with Integers

public class AbsIntExample {
    public static void main(String[] args) {
        int num1 = -25;
        int num2 = 15;
        int absValue1 = Math.abs(num1);
        int absValue2 = Math.abs(num2);

        System.out.println("Absolute of -25: " + absValue1);
        System.out.println("Absolute of 15: " + absValue2);
    }
}

Output:

Absolute of -25: 25  
Absolute of 15: 15

Explanation: Math.abs(-25) returns 25 by negating the negative value. Math.abs(15) remains 15 as it is already positive.

long Absolute Value Example

For large whole numbers, abs() handles long values, ensuring compatibility with applications involving big data, timestamps, and financial computations.

Math.abs Java Example: Using abs() with Long Values

public class AbsLongExample {
    public static void main(String[] args) {
        long num1 = -10000000000L;
        long num2 = 5000000000L;
        long absValue1 = Math.abs(num1);
        long absValue2 = Math.abs(num2);

        System.out.println("Absolute of -10000000000: " + absValue1);
        System.out.println("Absolute of 5000000000: " + absValue2);
    }
}

Output:

Absolute of -10000000000: 10000000000  
Absolute of 5000000000: 5000000000 

Explanation: Math.abs(-10000000000L) converts the large negative value to positive. Math.abs(5000000000L) remains unchanged.

float Absolute Value Example

For decimal numbers, abs() helps in mathematical computations, such as physics calculations, financial modeling, and graphics rendering.

Math.abs Java Example: Using abs() with Float Values

public class AbsFloatExample {
    public static void main(String[] args) {
        float num1 = -10.75f;
        float num2 = 3.25f;
        float absValue1 = Math.abs(num1);
        float absValue2 = Math.abs(num2);

        System.out.println("Absolute of -10.75: " + absValue1);
        System.out.println("Absolute of 3.25: " + absValue2);
    }
}

Output:

Absolute of -10.75: 10.75  
Absolute of 3.25: 3.25

Explanation: Math.abs(-10.75f) removes the negative sign. Math.abs(3.25f) remains unchanged.

double Absolute Value Example

Similar to float, the double version of abs() is used for high-precision calculations where absolute values of negative decimals need to be retrieved.

Math.abs Java Example: Using abs() with Double Values

public class AbsDoubleExample {
    public static void main(String[] args) {
        double num1 = -99.99;
        double num2 = 45.67;
        double absValue1 = Math.abs(num1);
        double absValue2 = Math.abs(num2);

        System.out.println("Absolute of -99.99: " + absValue1);
        System.out.println("Absolute of 45.67: " + absValue2);
    }
}

Output:

Absolute of -99.99: 99.99  
Absolute of 45.67: 45.67

Explanation: Math.abs(-99.99) removes the negative sign. Math.abs(45.67) remains the same.

Handling Edge Cases (Overflow and Negative Values)

Java's abs() method has a known limitation when handling the minimum integer (Integer.MIN_VALUE) and long (Long.MIN_VALUE) values.

Edge Case: Integer.MIN_VALUE and Long.MIN_VALUE

public class AbsEdgeCaseExample {
    public static void main(String[] args) {
        int minInt = Integer.MIN_VALUE;
        long minLong = Long.MIN_VALUE;

        System.out.println("Integer.MIN_VALUE: " + minInt);
        System.out.println("Math.abs(Integer.MIN_VALUE): " + Math.abs(minInt));

        System.out.println("Long.MIN_VALUE: " + minLong);
        System.out.println("Math.abs(Long.MIN_VALUE): " + Math.abs(minLong));
    }
}

Output:

Integer.MIN_VALUE: -2147483648  
Math.abs(Integer.MIN_VALUE): -2147483648  
Long.MIN_VALUE: -9223372036854775808  
Math.abs(Long.MIN_VALUE): -9223372036854775808

Explanation: When you call Math.abs(Integer.MIN_VALUE), it returns the same negative value, Integer.MIN_VALUE, because of how integers are represented in two's complement format. 

In this format, Integer.MIN_VALUE is -2147483648, and there is no corresponding positive value in the int range (the maximum is 2147483647). 

As a result, the operation causes an integer overflow rather than throwing an exception, and the absolute value of Integer.MIN_VALUE remains the same due to this limitation in the int data type.

How to Handle This? To safely handle Integer.MIN_VALUE, use a larger data type (long) to prevent overflow:

long safeAbs = Math.abs((long) Integer.MIN_VALUE);
System.out.println("Safe Absolute of Integer.MIN_VALUE: " + safeAbs);

Output:

Safe Absolute of Integer.MIN_VALUE: 2147483648

Also Read: Careers in Java: How to Make a Successful Career in Java in 2025

Now, let’s walk through some practical examples so you can get a feel for how to apply Math.abs() in real-world Java applications.

Practical Examples of Using abs() in Java

The Math.abs() method is widely used in real-world applications, making it a crucial function in Java programming. 

Whether it's for basic calculations, decision-making in conditions, or real-world applications in finance, gaming, and physics, abs() ensures that negative values are handled efficiently.

This section explores practical use cases of Math.abs(), from simple examples to more advanced applications.

Basic Example of Math.abs()

The simplest use of abs() is to convert a negative number into its positive counterpart while leaving positive numbers unchanged.

Example: Simple Absolute Value Calculation

public class AbsBasicExample {
    public static void main(String[] args) {
        int negativeInt = -20;
        int positiveInt = 15;
        double negativeDouble = -7.5;
        
        System.out.println("Absolute of -20: " + Math.abs(negativeInt));
        System.out.println("Absolute of 15: " + Math.abs(positiveInt));
        System.out.println("Absolute of -7.5: " + Math.abs(negativeDouble));
    }
}

Output:

Absolute of -20: 20  
Absolute of 15: 15  
Absolute of -7.5: 7.5

Explanation: Math.abs(-20) returns 20, and Math.abs(15) remains 15. Math.abs(-7.5) removes the negative sign and returns 7.5.

Using abs() in Conditional Statements

The abs() method is useful in conditions where a decision is based on the magnitude of a number rather than its sign.

Example: Checking Value Proximity

public class AbsConditionalExample {
    public static void main(String[] args) {
        int balance = -100;
        
        if (Math.abs(balance) > 50) {
            System.out.println("Your balance (absolute) is significant: " + Math.abs(balance));
        } else {
            System.out.println("Your balance is within a safe range.");
        }
    }
}

Output:

Your balance (absolute) is significant: 100  

Explanation: Math.abs(balance) converts -100 to 100, allowing the program to evaluate the absolute value without worrying about negative signs. This approach is useful in financial applications where only the magnitude matters (e.g., overdraft limits).

Finding the Absolute Difference Between Two Numbers

A common use case for abs() is computing the absolute difference between two numbers, ensuring a positive result regardless of their order.

Example: Distance Between Two Numbers

public class AbsDifferenceExample {
    public static void main(String[] args) {
        int num1 = 50;
        int num2 = 80;
        
        int difference = Math.abs(num1 - num2);
        
        System.out.println("The absolute difference between " + num1 + " and " + num2 + " is: " + difference);
    }
}

Output:

The absolute difference between 50 and 80 is: 30  

Explanation: num1 - num2 gives -30, but Math.abs(-30) returns 30, ensuring a non-negative result. This is useful in distance calculations (e.g., difference in stock prices, age gaps, or positional differences).

Applying abs() in Real-World Scenarios

The abs() method is widely used in finance, gaming, and physics for precise calculations.

1. Finance: Ensuring Positive Transaction Amounts

public class AbsFinanceExample {
    public static void main(String[] args) {
        double withdrawal = -150.75; // Representing a withdrawal
        double absoluteAmount = Math.abs(withdrawal);
        
        System.out.println("Transaction processed for amount: $" + absoluteAmount);
    }
}

Output:

Transaction processed for amount: $150.75

Explanation: Even if the withdrawal amount is negative, abs() ensures it's processed as a positive transaction. This is useful for accounting software where transaction values must always be positive.

2. Gaming: Calculating Player Distance

public class AbsGameExample {
    public static void main(String[] args) {
        int playerX = 10;
        int enemyX = 35;
        
        int distance = Math.abs(playerX - enemyX);
        
        System.out.println("Distance between player and enemy: " + distance + " units");
    }
}

Output:

Distance between player and enemy: 25 units  

Explanation: This is useful in game development, where distance calculations between objects are necessary for AI movement and collision detection.

3. Physics: Calculating Speed Difference

public class AbsPhysicsExample {
    public static void main(String[] args) {
        double initialSpeed = 15.2;
        double finalSpeed = 7.8;
        
        double speedChange = Math.abs(finalSpeed - initialSpeed);
        
        System.out.println("Speed difference: " + speedChange + " m/s");
    }
}

Output:

Speed difference: 7.4 m/s  

Explanation: Physics simulations often require absolute differences in velocity, force, or energy calculations.

4. Data Analysis: Finding the Closest Number to a Target

Imagine you have a list of integers, and you need to find the number closest to a given target (e.g., a prediction or a reference value). 

By calculating the absolute difference between each number in the list and the target, you can easily sort and pick the closest number.

import java.util.Arrays;
import java.util.Comparator;

public class ClosestNumber {
    public static void main(String[] args) {
        int[] numbers = {10, 15, 2, 8, 30};
        int target = 12;

        // Sort based on the absolute difference from the target
        Arrays.sort(numbers, Comparator.comparingInt(num -> Math.abs(num - target)));

        // Closest number to the target
        System.out.println("The closest number to " + target + " is: " + numbers[0]);
    }
}

Output:

The closest number to 12 is: 10

In this example, you sort the array based on the absolute differences from the target, and the closest number is at the first position in the sorted array.

5. Data Cleaning: Removing Negative Values

In data preprocessing, it's common to encounter negative values where they don't make sense (such as in datasets representing quantities like age, sales, or temperatures). Using the abs() method, you can clean up the data by converting negative values to positive ones.

Example: Cleaning a Dataset of Temperature Readings

Imagine you are working with a dataset containing temperature readings, but some values are mistakenly recorded as negative (indicating incorrect data input). You can use Math.abs() to correct these errors.

public class DataCleaning {
    public static void main(String[] args) {
        int[] temperatures = {-5, 23, -10, 35, 12};

        for (int i = 0; i < temperatures.length; i++) {
            temperatures[i] = Math.abs(temperatures[i]);  // Clean negative values
        }

        // Print cleaned dataset
        System.out.println("Cleaned temperature readings:");
        for (int temp : temperatures) {
            System.out.println(temp);
        }
    }
}

Output:

Cleaned temperature readings:

5
23
10
35
12

Here, the negative temperature values are cleaned up and converted to their absolute equivalents, ensuring the dataset makes sense for further analysis.

Also Read: What is Composition in Java With Examples 

While using Math.abs() is simple, it’s important to use it efficiently for better performance. In the next section, we’ll cover optimization tips, common mistakes, and best practices to ensure your code runs smoothly and efficiently. 

Performance and Best Practices for Using abs() in Java

The Math.abs() method is efficient and widely used for obtaining absolute values in Java. 

However, understanding its performance implications, avoiding common pitfalls, and knowing when alternative approaches are more suitable can improve overall efficiency and reliability in your applications.

This section covers the performance aspects of abs(), common mistakes to avoid, alternative ways to calculate absolute values, and best practices for using abs() efficiently.

Performance Considerations of abs()

The abs() method is highly optimized and runs in constant time O(1) since it only involves:

• A bitwise check for negative numbers.
• A single negation operation (-x) when needed.

Since it is implemented at the JVM level, it is as fast as manually writing if-else conditions for absolute value calculations.

Let’s compare the execution time of Math.abs() with a custom absolute function.

Example: Benchmarking Math.abs() vs. Custom Implementation

public class AbsPerformanceTest {
    public static int customAbs(int num) {
        return (num < 0) ? -num : num;
    }

    public static void main(String[] args) {
        int testValue = -1000000;
        long start, end;

        // Test Math.abs()
        start = System.nanoTime();
        int result1 = Math.abs(testValue);
        end = System.nanoTime();
        System.out.println("Math.abs() Time: " + (end - start) + " ns");

        // Test Custom Absolute Function
        start = System.nanoTime();
        int result2 = customAbs(testValue);
        end = System.nanoTime();
        System.out.println("Custom Abs Time: " + (end - start) + " ns");
    }
}

Expected Output (Varies Slightly Based on System):

Math.abs() Time: 30 ns  
Custom Abs Time: 35 ns

Math.abs() is slightly faster due to JVM optimizations. Custom implementations don't offer any significant advantage in performance. Use Math.abs() unless an alternative is explicitly required (e.g., handling Integer.MIN_VALUE).

Common Mistakes and How to Avoid Them

Even though Math.abs() is straightforward, some common mistakes can lead to unexpected behavior.

Mistake 1: Using Math.abs() on Integer.MIN_VALUE or Long.MIN_VALUE

Problem: Integer Overflow

public class AbsMistakeExample {
    public static void main(String[] args) {
        int minInt = Integer.MIN_VALUE;
        System.out.println("Math.abs(Integer.MIN_VALUE): " + Math.abs(minInt));
    }
}

Output:

Math.abs(Integer.MIN_VALUE): -2147483648

Integer.MIN_VALUE is -2147483648, but the maximum int can hold is 2147483647. The negation of -2147483648 exceeds the int range, causing an integer overflow and returning the same negative number instead of a positive one.

Solution: Use a Larger Data Type (long)

long safeAbs = Math.abs((long) Integer.MIN_VALUE);
System.out.println("Safe Absolute of Integer.MIN_VALUE: " + safeAbs);

Output:

Safe Absolute of Integer.MIN_VALUE: 2147483648

Mistake 2: Using Math.abs() for Unnecessary Cases

Problem: Applying abs() to Always Positive Numbers

double positiveValue = 10.5;
double absValue = Math.abs(positiveValue); // Unnecessary

Solution: Avoid using Math.abs() if the value is already guaranteed to be positive (e.g., predefined positive constants or values from a restricted range).

Alternative Approaches to abs() (Custom Implementations)

While Math.abs() is optimal in most cases, custom implementations can be useful in specific scenarios.

1. Using Bitwise Operations (For Integers Only)

Bitwise operations can be useful for performance optimization in low-level systems programming, but in Java, they are generally unnecessary. The Math.abs() method is already optimized, making it the most efficient approach for handling absolute values in typical Java applications. 

public class AbsBitwise {
    public static int bitwiseAbs(int num) {
        int mask = num >> 31; // Extract sign bit (0 for positive, -1 for negative)
        return (num ^ mask) - mask;
    }

    public static void main(String[] args) {
        System.out.println("Bitwise Absolute of -10: " + bitwiseAbs(-10));
          }
       }

Output:

Bitwise Absolute of -10: 10

Why Use This? Faster on some low-level hardware architectures due to reduced branching (if-else). Works only for integers, not for floating-point numbers.

2. Handling Integer.MIN_VALUE Without Overflow

public class SafeAbs {
    public static int safeAbs(int num) {
        return (num == Integer.MIN_VALUE) ? Integer.MAX_VALUE : Math.abs(num);
    }

    public static void main(String[] args) {
        System.out.println("Safe Absolute of Integer.MIN_VALUE: " + safeAbs(Integer.MIN_VALUE));
    }
}

Output:

Safe Absolute of Integer.MIN_VALUE: 2147483647

Why Use This? Prevents integer overflow when using Math.abs(Integer.MIN_VALUE).

Best Practices for Using abs() Efficiently

To ensure optimal performance, correctness, and maintainability, it's important to use Math.abs() effectively while avoiding common pitfalls. Here are some best practices to follow:

1. Prefer Math.abs() Over Custom Implementations: It is optimized and runs in constant time O(1). JVM optimizations make it as fast as manual checks.

2. Avoid Using abs() on Values Already Known to be Positive: Unnecessary calls can slightly affect performance in high-frequency operations.

3. Be Cautious with Integer.MIN_VALUE and Long.MIN_VALUE: Use a long cast before applying Math.abs() to prevent integer overflow.

4. Use abs() When Comparing Differences, Not Direction: For example, calculating distance, financial transactions, physics simulations.

5. For Performance-Sensitive Integer Computations, Consider Bitwise Operations: Faster in low-level applications, but rarely needed in high-level Java programs.

Also Read: Transient in java: What is, How Does it Work?

To solidify your understanding of Abs in Java, test your knowledge with a quiz. It’ll help reinforce the concepts discussed throughout the tutorial and ensure you're ready to apply them in your projects.

Quiz to Test Your Knowledge on Abs in Java

Assess your understanding of the abs() method in Java, its performance implications, and best practices by answering the following multiple-choice questions. Dive in!

1. What is the primary purpose of the Math.abs() method in Java?

a) To round off decimal values

b) To return the absolute (non-negative) value of a number

c) To convert integers to floating-point numbers

d) To find the maximum of two numbers

2. Which Java class provides the abs() method?

a) java.util.Math

b) java.lang.Math

c) java.math.BigDecimal

d) java.util.Arrays

3. What will Math.abs(-5.5) return?

a) -5.5

b) 5.5

c) 6

d) -6

4. Which data types are supported by the Math.abs() method?

a) int, long, float, and double

b) char, int, float, and String

c) boolean, int, float, and double

d) short, byte, char, and int

5. What happens when Math.abs(Integer.MIN_VALUE) is called?

a) It returns 2147483648

b) It throws an ArithmeticException

c) It returns -2147483648 (unchanged due to integer overflow)

d) It returns Integer.MAX_VALUE

6. How can you safely get the absolute value of Integer.MIN_VALUE without overflow?

a) Use Math.abs(Integer.MIN_VALUE) directly

b) Cast it to long before applying Math.abs()

c) Use Math.sqrt(Integer.MIN_VALUE)

d) Multiply it by -1

7. Which of the following is NOT a best practice for using Math.abs()?

a) Avoid using abs() when the value is already known to be positive

b) Use Math.abs() for magnitude comparisons rather than directional logic

c) Always use abs() on Integer.MIN_VALUE

d) Consider bitwise operations for performance-critical integer calculations

8. What is the time complexity of Math.abs() in Java?

a) O(log n)

b) O(n)

c) O(1)

d) O(n²)

9. When is using Math.abs() particularly useful?

a) When checking if a number is even or odd

b) When computing distances between two points

c) When performing string comparisons

d) When converting an integer to a string

10. Which of the following alternative implementations of abs() is the most optimized for integers?

a) return (num < 0) ? -num : num;

b) return Math.pow(num, 2);

c) return num & Integer.MAX_VALUE;

d) return num / -1;

Also Read: Top 8 Reasons Why Java Is So Popular and Widely Used in 2025

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FAQs

Q: Can Math.abs() handle negative zero (-0.0)?

A: Yes, Math.abs(-0.0) returns 0.0, as Java treats negative and positive zero as equivalent in most cases. However, -0.0 may still behave differently in certain floating-point operations, such as division or comparisons, where its sign can persist.

Q: Does Math.abs() modify the original variable?

A: No, Math.abs() does not alter the original variable; it simply returns a new absolute value. To store the result, you must assign it back to the variable, like num = Math.abs(num);, otherwise, the value remains unchanged.

Q: Can Math.abs() be used with custom objects?

A: No, Math.abs() only works with primitive numeric types (int, long, float, and double). If you need absolute values for custom objects, such as vectors or financial transactions, you must implement a separate method to handle the computation.

Q: How does Math.abs() behave with NaN (Not-a-Number)?

A: If you pass Float.NaN or Double.NaN to Math.abs(), it will return NaN. This behavior follows the IEEE 754 floating-point standard, which ensures that NaN (Not-a-Number) propagates through calculations without being altered. 

Q: Is Math.abs() thread-safe?

A: Yes, Math.abs() is thread-safe because it is a pure function—it does not modify shared state or depend on external variables. Even in multi-threaded applications, calling Math.abs() will always return the correct absolute value without causing race conditions.

Q: Can Math.abs() be used in a loop efficiently?

A: Yes, Math.abs() runs in constant time O(1) and is highly optimized. However, repeatedly calling it inside a loop on the same value is unnecessary. If an absolute value is used multiple times, store it in a variable to avoid redundant computations.

Q: How does Math.abs() handle floating-point precision errors?

A: Math.abs() does not correct floating-point rounding errors that result from binary representation limitations. If a floating-point number has slight inaccuracies (e.g., 0.30000000000000004 instead of 0.3), abs() will return the absolute value with the same level of precision error.

Q: Can Math.abs() be overloaded for custom data types?

A: No, Java does not allow overloading the Math.abs() method. However, you can create a custom method in your class, such as public static MyClass abs(MyClass obj), to define absolute value behavior for user-defined types like complex numbers or matrices.

Q: What happens if Math.abs() is applied to an expression?

A: When Math.abs() is used on an expression, Java evaluates the expression first, then applies abs(). For example, Math.abs(10 - 20) computes -10 first, and then returns 10. This makes it useful for computing absolute differences dynamically.

Q: Does Math.abs() introduce any performance overhead?

A: In most cases, Math.abs() has negligible performance impact as it runs in constant time. However, in performance-critical applications such as graphics rendering, physics engines, or real-time simulations, reducing unnecessary calls can slightly improve efficiency.

Q: Can Math.abs() be used for complex numbers?

A: No, Math.abs() does not support complex numbers directly. To compute the absolute value (magnitude) of a complex number, you need to use Math.sqrt(real² + imaginary²), or rely on libraries like Apache Commons Math, which provide built-in complex number operations.

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