SOLUTION: Find {{{(-(sqrt(3)/2)+(i/2))^91}}} by changing it to polar form and then applying De Moivre's Theorem. Give your simplified answer in rectangular form. Use exact values

Algebra ->  Trigonometry-basics -> SOLUTION: Find {{{(-(sqrt(3)/2)+(i/2))^91}}} by changing it to polar form and then applying De Moivre's Theorem. Give your simplified answer in rectangular form. Use exact values      Log On


   

Question 762274: Find %28-%28sqrt%283%29%2F2%29%2B%28i%2F2%29%29%5E91 by changing it to polar form and then applying De Moivre's Theorem. Give your simplified answer in rectangular form. Use exact values
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find %28-%28sqrt%283%29%2F2%29%2B%28i%2F2%29%29%5E91 by changing it to polar form and then applying De Moivre's Theorem. Give your simplified answer in rectangular form. Use exact values
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Ok
What did you get for the magnitude?

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






Since , and we know that and , it is evident that and

From the unit circle we deduce

So we now have



Then De Moivre says:



So



Since , that falls off. Then , so:





John

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