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

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Answer 1 · 2015-11-04T20:05:18

$-32i$

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

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

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

$=-32i$

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