Additive Inverse

An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, $a$ is the original number, then its additive inverse will be minus of $a$ i.e.,$-a$, such that;

$a+(-a)=a-a=0$

The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign.

For example, the additive inverse of $8$ is $-8$, whereas the additive inverse of $-8$ is $8$..

Additive inverse of Natural or Whole Numbers

Natural numbers are the positive integers. Therefore, the additive inverse of positive integers will be negative.

Natural or Whole Numbers	Additive inverse	Result
$10$	$-10$	$10+(-10)=0$
$20$	$-20$	$20+(-20)=0$
$30$	$-30$	$30+(-30)=0$

Additive Inverse of Rational Numbers

Suppose ${\frac {a}{b}}$ is a rational number such that the additive inverse of ${\frac {a}{b}}$ is $-{\frac {a}{b}}$and vice versa.

Fraction	Additive inverse	Result
${\frac {1}{2}}$	$-{\frac {1}{2}}$	${\frac {1}{2}}+(-{\frac {1}{2}})=0$
${\frac {3}{4}}$	$-{\frac {3}{4}}$	${\frac {3}{4}}+(-{\frac {3}{4}})=0$
${\frac {5}{7}}$	$-{\frac {5}{7}}$	${\frac {5}{7}}+(-{\frac {5}{7}})=0$

Additive Inverse of Complex Numbers

Complex numbers are the combination of real numbers and imaginary numbers. $a+ib$ is a complex number, where $a$ is the real number and $ib$ is the imaginary number.

The additive inverse of $a+ib$ should be a value, that on adding it with a given complex number, we get a result as zero. Therefore, it will be $-(a+ib)$

Example: Additive inverse of $4+5i$ is $-(4+5i)$

$4+5i+[-(4+5i)]$

$4+5i-4-5i=0$

Difference Between Additive Inverse and Multiplicative Inverse

Additive Inverse	Multiplicative Inverse
It is added to the original number to get $0$	It is multiplied to the original number to get $1$
Results in $0$	Results in $1$
Sign of the original number is changed and added	Reciprocal of the original number is multiplied
Example: $55+(-55)=0$	Example: $55\times {\frac {1}{55}}=1$