Question

Find all complex numbers $z$ which satisfy the following equation
$z=-\overline{z}$

• A. All pure real numbers.
• B. All numbers.
• C. All pure imaginary numbers.
• D. Not defined

Answer 1

Answer: (C)

All pure imaginary numbers.

Given $z=-\overline{z}$

$⟹z+\overline{z}=0$

Let $z=a+ib$ ; so $\overline{z}=a-ib$

$⟹a+ib+a-ib=0$

$⟹2a=o⟹a=0$

So, $z=a+ib=0+ib=ib$, which is purely imaginary number.