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.

9514 1404 393

  {2, 2i, -2, -2i}

Step-by-step 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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

20

step-by-step explanation: