Question

The complex number z satisfies $z+\left|z\right|=2+8i$. The value of ($\left|z\right|-8)$ is

Answer 1

Put $z=x+iy$
$\Rightarrow x+iy+\sqrt{x^2+y^2}=2+8i$
$\Rightarrow y=8$ and $x+\sqrt{x^2+y^2}=2$
$\Rightarrow x^2+y^2=(2-x{)}^2=4-4x+x^2$
$\Rightarrow 4x=4-y^2=-60\Rightarrow x=-15$
$\Rightarrow z=-15+8i\therefore |z|=\sqrt{{15}^2+8^2}=17$