Complex numbers

Is there any other easy method than algebraic method ??


Can u explain what u did in z=1?

@harishr square both sides so dat $∣z∣_{2}=1$
Now $∣z∣_{2}=zz_{′}=1$ where $z_{′}$ is conjugate of $z$
So $z_{′}=1/z$
Substitute dis in $z_{3}+z_{′}=0$