The number that is added to a given number in order to make the sum zero is known as the additive inverse. If we add -3 to the number 3, we get zero. As a result, the inverse additive of 3 is -3. In our daily lives, we come across circumstances where we take the additive inverse of a quantity to invalidate its value. In this post, we’ll look at how real and complex numbers have additive inverse properties.

## Definition:-

The value of the additive inverse of a number is defined as the value that when added to the original number yields zero. It is the number we add to the number to make it equal zero. If a is an original number then the additive inverse of a is -a, as follows

a + (-a) = 0

Example: Additive inverse of 11 is -11

Additive inverse of -0.7 is 0.7

The opposite of a number, negation of a number, or changed sign of an original number are all terms used to describe additive inverse.

### Methods to find out additive inverse:-

By altering the sign of any given number, the additive inverse can be found. A positive number’s additive inverse will be negative, whereas a negative number’s additive inverse will be positive. The numerical value, however, will not change except for the sign. The additive inverse of 8 is, for example, -8, but the additive inverse of -8 is 8

The additive identity is equal to the sum of an integer and its additive inverse.

### Properties of additive inverse:-

To get an value equal to 0, additive inverse simply implies changing the sign of the number and adding it to the original number.

The qualities of additive inverse, based on negation of the original number, are listed below. If x is the original number, then -x is the additive inverse. So, let’s look at the features of -x.

- −(−x) = x
- (-x)² = x²
- −(x + y) = (−x) + (−y)
- −(x – y) = y – x
- X – (−y) = x + y
- (−x) × y = x × (−y) = −(x × y)
- (−x) × (−y) = x × y

### Additive Inverse of Different Numbers:-

We’ve learned that an additive inverse is used to reduce a value to zero. This value can now be any of the following: a natural number, an integer, a rational number, an irrational number, a complex number, and so on. Let’s look for the additive inverse of several numbers.

- Natural or Whole Numbers’ additive inverse:

Natural numbers are positive integers, as we all know. As a result, the inverse additive of positive integers will be negative.

- Additive inverse of Complex Numbers:

Complex numbers are made up of both real and imaginary numbers. A complex number is A + iB, where A is the real number and B is the imaginary number.

Now, the additive inverse of A + iB must be a value that, when multiplied by a given complex integer, equals zero. As a result, it’ll be –(A + iB).

Example: Additive inverse of 5 + 4i is –(5 + 4i) as

5+4i – (5+4i) = 0

- Additive inverse of rational numbers:

Assume that a/b is a rational number, and that its additive inverse is -a/b, and vice versa.

For example the additive inverse of -2/3 is 2/3 as

-2/3 + 2/3 = 0

- Additive inverse of algebraic expressions:

Algebraic expressions can benefit from the additive inverse characteristic. The additive inverse of an algebraic expression is one that makes the total of all terms zero, following the same rule as previously stated. Observe that the expression’s additive inverse is -. (expression). – (x³ + 1) = -x³ – 1 is the additive inverse of x³ + 1

The additive inverse of 6x – y, for example, is -6x + y, which equals zero.

### General formula of additive inverse:-

The generic formula for a number’s additive inverse can be written as the number itself. When a positive number is added to its negative, the two cancel each other out, resulting in a total of zero. The negative of the provided number N must be found. To put it another way, we need to discover -1. (N). As a result, we can state:

Inverse Additive of N = -1 ×(N)

### Conclusion:-

The number we add to a number to make the sum zero is called additive inverse. The additive inverse of 13 is -13, because their sum is zero. When two numbers are added together to give 0, we say that they are additive inverses of one another.

Understanding how to cancel terms when solving for variables in equations and formulas requires understanding inverses such as the additive inverse and multiplicative inverses. When you add a number to its additive inverse, you get zero. This is helpful for removing terms.