First slide

Algebra of complex numbers

Question

The number of solutions of $z^{2} + | z | = 0$ is

Moderate

A

1
B

2
C

3
D

infinite

Solution

$\begin{array}{l} |z^{2}| = | - | z | | \Rightarrow | z |^{2} = | z | \\ \Rightarrow | z | = 0 or | z | = 1 \\ If | z | = 0, we get z = 0 . If | z | = 1 \\ we get z^{2} = - 1 \Rightarrow z = \pm i \end{array}$

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