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Expert: - 2/15/2010


Question
simplify (2-2i)^5 with de Moivres formula

thank you in advance

Answer
Questioner: Kamila
Country: Sweden
Category: Advanced Math
Private: No
Subject: complex numbers
Question: simplify (2-2i)^5 with de Moivres formula

thank you in advance
.................................
Start by writing  2 - 2i in 'polar form':  Find your r = 2 sqrt(2) and  theta = -pi/4 or 7pi/4.

Then apply de Moivre's theorem:

[2 sqrt(2) cis(-pi/4)]^5 =

[2 sqrt(2)]^5 cis (-5pi/4)

Work out the r.

Diagram the -5pi/4  or  3pi/4.  

Convert that back to rectangular form.  

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