Question

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

• A. $1$
• B. $2$
• C. $3$
• D. Infinite

Answer 1

Answer: (C)

$3$

$\to z^2+\left|z\right|=0$

Let $z=r{e}^{i\theta }$

$\to r^2{e}^{2i\theta }+r=0$

$\to r(r{e}^{2i\theta }+1)=0$

So, either $r=0$ or $r{e}^{2i\theta }=-1$

$r{e}^{2i\theta }=-1\Rightarrow r=1$ & $2\theta =\pi +2n\pi$

We get $z=0$ or $z=i$ or $z=-i$

Therefore, $3$ solutions are possible.