# How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?

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May 19, 2016

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Divide by the norm of

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De Moivre's formula, which can be derived from Euler's formula that

However, as

#=(sqrt(2))^20(sqrt(2)/2+sqrt(2)/2i)^20#

#=1024(cos(pi/4)+isin(pi/4))^20#

#=1024(cos(20*pi/4)+isin(20*pi/4))#

#=1024(cos(5pi)+isin(5pi))#

#=1024(-1+i*0)#

#=-1024#

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