Question

The number of solution of the equation $z^2+|z{|}^2=0$, where $Z\in C$ is

• A. one
• B. two
• C. three
• D. infinitely many

Answer 1

The correct option is B two

Let $z=r{e}^{i\theta }$ (euler form)

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

$\Rightarrow e^{2i\theta }+1=0$

We know $e^{2i\theta }=\cos 2\theta +i\sin 2\theta =-1$

$\Rightarrow \cos 2\theta =-1,\sin 2\theta =0$

Solutions are $\theta =\frac{\pi }{2},\frac{-\pi }{2}$

So, two solution exist for this equation.