Question

What is the number of distinct solutions of the equation $z^2+|z|=0$ (where z is a complex number)?

• A. One
• B. Two
• C. Three
• D. Five

Answer 1

The correct option is C Three

$Letz=r{e}^{i\theta }$

$\therefore r^2{e}^{2i\theta }+r=0$ $\therefore r=0orr{e}^{2i\theta }=-1$

$\therefore For,r{e}^{2i\theta }=-1,$

$r=1and2\theta =\pi +2n\pi$

$\therefore z=iorz=-i$

$andwehadr=0,thus,z=0.$

$\therefore Threesolutions.$