Question

The number of solutions of the equation
$z^2+|z{|}^2=0$ where $z\epsilon \text{C}$ is

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

Answer 1

The correct option is D infinitely many

Let z = x + iy, then
$z^{2}2+|z{|}^2=0\Rightarrow (x+iy{)}^2+|x+iy{|}^2=0$
$\Rightarrow x^2-y^2+2ixy+x^2+y^2=0$
$\Rightarrow 2x^2+2ixy=0$
Clearly y can be any real number hence, we will get infinitely many solutions