Question

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

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

Answer 1

The correct option is B Two

Let $z=x+iy{z}^2=x^2-y^2+2xyi$

$|z|=\sqrt{x^2+y^2}|z{|}^2=x^2+y^2{x}^2-y^2+2xyi+x^2+y^2=02x^2+2xyi=02x(x+yi)=0x=0orx=-yi$

$\therefore 2$ Solutions.