Question

The number $16$ has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below:\[\square^4=16.\] Find them.

Answer 1

9514 1404 393

Answer:

{2, 2i, -2, -2i}

Explanation:

Fourth roots of positive real numbers are always on the cardinal points of the complex plane. The positive real fourth root of 16 = 2^4 is 2. The others are this multiplied by various powers of i.

2, 2i, -2, -2i