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: [blank]^4 = 16. Find them.

Guest Jan 10, 2021

#1**+1 **

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: [blank]^4 = 16. Find them.

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\(\{\sqrt[4]{16}\}=\{\sqrt{4},\sqrt{-4}\}=\color{blue}\{2,-2,2i,-2i\}\)

\(2^4=16\\ (-2)^4=16\\ (2i)^4=16\\ (-2i)^4=16\)

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asinus Jan 11, 2021