Question

If $z$ is a complex number such that $z=-\overline{z}$, then.

• A. $z$ is purely real
• B. $z$ is purely imaginary
• C. $z$ is any complex number
• D. Real part of $z$ is the same as its imaginary part

Answer 1

The correct option is B $z$ is purely imaginary

let the complex number $z=a+ib$

where $a$ is real part and $b$ is imaginary part.

$-\overline{z}=-(a-ib)=-a+ib$

So if $z=-\overline{z}$

$\Rightarrow a+ib=-a+ib$

$\Rightarrow 2a=0,a=0$

Since $a$ is zero, $z$ is purely imaginary number