Question

Indicate the point of the complex plane $z$ which satisfy the following equation.
$|z|+z=0$

Answer 1

Let $z=x+iy$

$|z|=\sqrt{x^2+y^2}$

$|z|+z=0$

$\sqrt{x^2+y^2}$$+x+iy=0$

$\sqrt{x^2+y^2}$$+x=0$ and $y=0$

$⟹{\sqrt{x}}^2+x=0$

$⟹2x=0$

$⟹x=0$