First slide

Algebra of complex numbers

Question

If $z \neq 0$ is a complex number such that $R e (z) = 0,$ then

Moderate

A

$Re (z^{2}) = 0$
B

$Im (z^{2}) = 0$
C

$Re (z^{2}) = Im (z^{2})$
D

$Im (z^{2}) < 0$

Solution

Let $z = b i, b \in R, b \neq 0,$
Then $z^{2} = - b^{2} \in R$
Therefore , $Im (z^{2}) = 0$

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