sagegoldstein1000 sagegoldstein1000

22-12-2020
Mathematics

contestada

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.

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sqdancefan sqdancefan

01-01-2021

9514 1404 393

Answer:

{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

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