SOLUTION: Perform the indicated operation, and enter your answer in standard form: (3*(cos(60°)+isin(60°)))^4 Thank you kindly.

Algebra ->  Trigonometry-basics -> SOLUTION: Perform the indicated operation, and enter your answer in standard form: (3*(cos(60°)+isin(60°)))^4 Thank you kindly.      Log On


   

Question 984827: Perform the indicated operation, and enter your answer in standard form:
(3*(cos(60°)+isin(60°)))^4
Thank you kindly.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2A%28cos%2860%29%2Bi%2Asin%2860%29%29%29%5E4


%283%29%5E4%2A%28cos%284%2A60%29%2Bi%2Asin%284%2A60%29%29 Use De Moivre's Theorem


81%2A%28cos%28240%29%2Bi%2Asin%28240%29%29


81%2A%28-1%2F2%2Bi%2A%28-sqrt%283%29%2F2%29%29 Use a unit circle or trig table


81%2A%28-1%2F2%29%2B81%2Ai%2A%28-sqrt%283%29%2F2%29


-81%2F2-%28%2881%2Asqrt%283%29%29%2F2%29i


-40.5-70.14806i


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The exact answer as a fraction is -81%2F2-%28%2881%2Asqrt%283%29%29%2F2%29i. Notice it is in the form a%2Bbi where a+=+-81%2F2 and b+=+-%2881%2Asqrt%283%29%29%2F2


The approximate answer is -40.5-70.14806i. Notice it is in the form a%2Bbi where a+=+-40.5 and b+=+-70.14806 (rounded to 5 decimal places)