SOLUTION: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form: [1/2(cos pi/10 + i sin pi/10)]^5

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form: [1/2(cos pi/10 + i sin pi/10)]^5      Log On


   

Question 88099: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form:
[1/2(cos pi/10 + i sin pi/10)]^5
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
According to DeMoive's Theorem
%281%2F2%29%28cos+%28pi%2F10%29+%2B+i+sin+%28pi%2F10%29%29%5E5
=%28%281%2F2%29%5E5%28cos+%285%2Api%2F10%29+%2B+i+sin%285%2Api%2F10%29%29%29
=%28%281%2F32%29%28cos+%28pi%2F2%29+%2B+i+sin%28pi%2F2%29%29%29

Now, cos%28pi%2F2%29=0 and sin%28pi%2F2%29=+1
=%28%281%2F32%29%28cos+%28pi%2F2%29+%2B+i+sin%28pi%2F2%29%29%29
=%28%281%2F32%29%280+%2B+i+%2A1%29%29
= i%2F32 or %281%2F32%29%2Ai

R^2