Question

Hi! Can anyone helps me with a problem?
Solve for z, where z is complex number
z^2 + |z| = 0

Answer 1

rewrite to -z^2=|z|
The real solution is z=0
the complex solutions are x=-i, i

Answer 2

Try sub z=i
LHS: -i^2=-(-1)=1
RHS: | i |=| sqrt(-1)|=sqrt|-1|=sqrt(1)=1

It works similarly for z=-i