Question

Solve the system of equations re $\left(z^2\right)=0,|z|=2$

Answer 1

Let $z:x+iy$

re $\left(z^2\right)=re\left[\right(x+iy\left)\right(x+iy\left)\right]$

$=re[x^2-y^2+2ixy]$

$\Rightarrow x^2-y^2=0$

x = y x = -y ...(1)

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

$\Rightarrow x^2+y^2=4$

for x = y for x = -y

x=$\sqrt{2},y=\sqrt{2}$ $x=-\sqrt{2},y=\sqrt{2}$

$x=-\sqrt{2},y=-\sqrt{2}$ $x=\sqrt{2},y=-\sqrt{2}$