Question

The multiplicative inverse of the complex number $503-4i$ is $x+iy$ the value of $x$ is

• A. $\frac{3}{50}$
• B. $\frac{4}{50}$
• C. $\frac{1006}{253025}$
• D. $\frac{503}{253025}$

Answer 1

The correct option is D $\frac{503}{253025}$

Multiplicative inverse of $a+ib=\frac{1}{a+ib}=\frac{a-ib}{a^2+b^2}$

Given,

$503-4i$

$=\frac{1}{503-4i}=\frac{503+4i}{{503}^2+4^2}$

$=\frac{503}{253025}+i\frac{4}{253025}$

$=x+iy$

$\therefore x=\frac{503}{253025}$