[Math] Find all complex numbers $z$ satisfying $|z+2i| = |z-2|$

Question

I am facing a small math problem. I need to find all complex numbers $z$ satisfying the equation $|z+2i| = |z-2|$.

I'd be very grateful if someone could "teach" me how to solve this one.

Best regards,
Janno

Answer 1

your complex number should be on the perpendicular bisector of -2i and 2 as you can see if you think them as points of plane.