Question

The multiplicative inverse of a non-zero complex number $z$ is

• A. $\frac{z}{|z{|}^2}$
• B. $\frac{\overline{z}}{|z{|}^2}$
• C. $\frac{\overline{z}}{|z|}$
• D. $\frac{z}{|z|}$

Answer 1

The correct option is B $\frac{\overline{z}}{|z{|}^2}$

Multiplicative inverse of a non-zero complex number $z$ is
$\frac{1}{z}=\frac{\overline{z}}{z\overline{z}}=\frac{\overline{z}}{|z{|}^2}(\because z\overline{z}=|z{|}^2)$