Complex numbers

Let

a=x+iy,z = mi

Substitute these values in the equation.

(-xm^2+1)+i(-m^2y+m)=0

\rightarrow x=y^2

|a|=1
\rightarrow x^2+y^2=1
\rightarrow x^2+x-1=0
\rightarrow x=\frac{-1\pm \sqrt{5}}{2}

x>0 since y has to be real.

x=\frac{\sqrt{5}-1}{2}\qquad y=\sqrt{\frac{\sqrt{5}-1}{2}}

http://goiit.com/posts/list/algebra-help-needed-in-a-question-of-complex-numbers-1199242.htm