2017/005) Solve $|z+1| = z+ 2 + 2|$

because LHS is real so z + 2i is real and let z + 2i = x or z = x - 2i
so |x+1 - 2i |= x +2|
or $(x+1)^2 + 4 = (x+2)^2$
or $x^2 + 2x + 5 = x^2 + 4x + 4$ or $x = \frac{1}{2}$
$z = \frac{1}{2} - 2i$