Question

Find the multiplicative inverse of 1/(4-3i)

Answer 1

Hi,

Solution:

As we know that multiplicative inverse of real number N = 1/N,

By the same way multiplicative inverse of complex number Z= 1/Z

Here
$z = \frac{1}{4 - 3i}$
Multiplicative inverse is 1/z

$\frac{1}{z} = \frac{1}{ \frac{1}{4 - 3i} } \\ \\ = 4 - 3i$
Multiplicative inverse of
$\frac{1}{4 - 3i}$

is
$4 - 3i$

Hope it helps you.

Answer 2

we know about multiplicative inverse , when any number X is given then 1/X is known as multiplicative inverse.

or you can say that if product of two different number is 1 then, one is multiplicative inverse of other.
for example :- 3/5 is multiplicative inverse of 5/3 . because 3/5 × 5/3 = 1

here complex number , $\mathbb{Z}=\frac{1}{4-3i}$
so, multiplicative inverse of $\mathbb{Z}$ is $\frac{1}{\mathbb{Z}}$

$\frac{1}{\mathbb{Z}}=\mathbb{Z}^{-1}=(4-3i)$