Question

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?

Answer 1

9514 1404 393

Answer:

2 -i

Explanation:

The two diagonals have the same center point. Here, it is ...

(1 +2) +(-1 -2i) = 0 +0i

The fourth point is found by reflecting the 2nd point across the origin:

p4 = -p2 = -(-2 +i) = 2 -i . . . . . fourth corner of the square