Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are -19+32i, -5+12i and -22+15i. What is the fourth number?
Just set up as coordinates in the real plane
(-19, 32) = A
(-5, 12) = C
Note that from B to C, x changes by 17 and y changes by -3
So the remaining coordinate = (-19 + 17, 32 - 3) = (-2, 29) = D
Expressing this in complex form = -2 + 29i
See here :