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# complex numbers

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Find all complex numbers z such that z^4 = 4.

Dec 27, 2020

#1
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Find all complex numbers z such that z^4 = 4.

Since it is a power of 4, there will be 4 solutions.

one of those solutions will be  $$\pm \sqrt[4]{ 4}=\pm \sqrt{2}$$

the other 2 will be   $$\pm \sqrt[4]{ 4}i=\pm \sqrt{2}\;i$$

Dec 28, 2020