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Evaluate (1+sqrt(3)i)^12 using DeMoivre's theorem. plz show all work

 Feb 3, 2023
edited by Guest  Feb 3, 2023
 #1
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Converting to polar form, we get 1 + sqrt(3)*i = sqrt(2)(cos 60 + i sin 60).

 

Then (1 + sqrt(3)*i)^12 = sqrt(2)^12 (cos 60 + i sin 60)^12

= 64 (cos 720 + i sin 720)

= 64

 

The answer is 64.

 Feb 3, 2023
 #2
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Like so:

 

 Feb 3, 2023

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