1. What is Additive Inverse?

The additive inverse of a number is a value that, when added to the original number, results in zero. For any number x, its additive inverse is -x.

2. How Does the Calculator Work?

The calculator uses the additive inverse formula:

Where:

• \( x \) — The original number

Explanation: The additive inverse is simply the negative of the original number. For example, the additive inverse of 5 is -5, and the additive inverse of -3 is 3.

3. Importance of Additive Inverse

Details: Additive inverses are fundamental in mathematics, particularly in algebra and arithmetic operations. They are essential for solving equations, simplifying expressions, and understanding the concept of opposites in number systems.

4. Using the Calculator

Tips: Enter any real number (positive, negative, or zero) to calculate its additive inverse. The result will be the number that, when added to your input, equals zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the additive inverse of zero?
A: The additive inverse of zero is zero itself, since 0 + 0 = 0.

Q2: Does every number have an additive inverse?
A: Yes, every real number has an additive inverse. For any number x, there exists -x such that x + (-x) = 0.

Q3: How is additive inverse different from multiplicative inverse?
A: Additive inverse results in zero when added to the original number, while multiplicative inverse results in one when multiplied by the original number (for non-zero numbers).

Q4: Can additive inverse be applied to complex numbers?
A: Yes, the additive inverse of a complex number a + bi is -a - bi.

Q5: What are some practical applications of additive inverse?
A: Additive inverses are used in balancing equations, financial calculations (debits/credits), physics (opposing forces), and computer science (two's complement representation).