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
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Question 762274: Find 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) (Show Source): You can put this solution on YOUR website!
Find 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) (Show Source): You can put this solution on YOUR website!
^{91})
^2\ +\ \left(\frac{1}{2}\right)\ =\ \frac{3}{4}\ +\ \frac{1}{4}\ =\ 1)
Since 
, and we know that 
and 
, it is evident that 
and 
From the unit circle we deduce 
So we now have
^{91})
Then De Moivre says:
\ +\ i\sin(\alpha)\right)^n\ =\ r^n\left(\cos(n\alpha)\ +\ i\sin(n\alpha)\right))
So
\right)\ +\ i\sin\left(91\left(\frac{5\pi}{6}\right)\right)\right))
Since , that falls off. Then 
, so:
\ +\ i\sin\left(\frac{11\pi}{6}\right)\ =\ \frac{\sqrt{3}}{2}\ -\ i\frac{1}{2})
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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