How do I use DeMoivre's theorem to find #(1-i)^10#?

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Nov 4, 2015

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#-32i#

Explanation:

First write this complex number in polar form and then apply De Moivre :

#(1-i)^10=(sqrt2/_-pi/4)^10=[sqrt2(cos(-pi/4)+isin(-pi/4))]^10#

#=(sqrt2)^10[cos(-10pi/4)+isin(-10pi/4)]#

#=-32i#

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