Question

Solve the equation z^2 = z , where z = x + iy

Answer 1

If z2 + |z| = 0, then z2 = -|z|. aking the modulus on both sides, |z2| = |z|, or |z|2 = |z|. Hence, |z| = 0 or 1. If |z| = 0, then z = 0. If |z| = 1, then z^2 = -1, resulting in z = ±i. So the solutions are 0, i, -i.