Question

If $z$ is a unimodular complex number, then its multiplicative inverse is,

• A. $\overline{z}$
• B. $z$
• C. $-z$
• D. $-\overline{z}$

Answer 1

The correct option is A $\overline{z}$

Since z is unimodular

$\Rightarrow |z|=1$

Multiplicative inverse of $z=\frac{1}{z}$

Multiplying both numerator and denominator by $\overline{z}$

$\frac{1}{z}$. $\frac{\overline{z}}{\overline{z}}$ = $\frac{\overline{z}}{{|z|}^2}$

$=\overline{z}$ ....(Since z is unimodular)

Thus, Option A is correct.