Multiplicative inverse

The multiplicative inverse of a number, say, $N$ , is represented by ${\frac {1}{N}}$ or $N^{-1}$ . It is also called reciprocal. The meaning of inverse is something which is opposite. The reciprocal of a number obtained is such that when it is multiplied by the original number, the value equals identity $1$ .

Multiplicative Inverse of Natural Number


Number	Multiplicative Inverse
$3$	${\frac {1}{3}}$
$15$	${\frac {1}{15}}$

Now to check whether the inverse of a number is correct or not, we can perform the multiplication operation, such that

$3\times {\frac {1}{3}}=1$ ........... $15\times {\frac {1}{15}}=1$

In the above cases we get the identity number $1$ . Hence it is proved.

Multiplication Inverse of Fraction

If ${\frac {p}{q}}$ is a fraction, then the multiplicative inverse of ${\frac {p}{q}}$ should be such that, when it is multiplied to the fraction, then the result should be $1$ . Hence, ${\frac {q}{p}}$ is the multiplicative inverse of fraction ${\frac {p}{q}}$ .

${\frac {p}{q}}\times {\frac {q}{p}}=1$

Number	Multiplicative Inverse
${\frac {3}{5}}$	${\frac {5}{3}}$
${\frac {15}{7}}$	${\frac {7}{15}}$

Multiplicative Inverse of Complex Numbers

For example, $4+{\sqrt {-3}}$ is a complex number.

since $i={\sqrt {-1}}$ It can be written as follows;

$4+i{\sqrt {3}}$

Here $4$ is the real number and $i{\sqrt {3}}$ is the imaginary number. Now to find the reciprocal of this complex number, we have to multiply and divide it by $4-i{\sqrt {3}}$ such that: