First slide

Algebra of complex numbers

Question

Let $z \in C$ be such that $R e (z^{2}) = 0$ , then

Easy

A

$| Re (z) | + Im (z) = 0$
B

$| Re (z) | = | Im (z) |$
C

$Re (z) + | Im (z) | = 0$
D

$Re (z) = 0 or Im (z) = 0$

Solution

Let $z = x + i y,$ then $z^{2} = x^{2} - y^{2} + 2 i x y$
$∴ Re (z^{2}) = 0 \Rightarrow x^{2} - y^{2} = 0$
$\Rightarrow | Re (z) | = | Im (z) |$

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