Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are 1+2i,-2+i and -1-2i. What is the fourth number?

Question

(A) 2+ i (B) 2-i (C) 1-2i (D) -1+2i (E) -2-i

Answer 1

idk

Answer 2

If we label the points A,B,C in the order given, then
A-B = 3+i
so D = C + 3+i = 2-i

to double-check, look at the slopes to be sure the sides are ⊥