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Express the given complex number in the form $\;a+ib : (1-i)^{4}$

$(a)\;2\qquad(b)\;-2i\qquad(c)\;4i\qquad(d)\;-4$

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Answer : $\;-4$
Explanation :
$(1-i)^{4} = [(1-i)^2]^2$
$ = [1^2 + i^2-2i]^2$
$= (-2i)^2$
$= (-2i) \times (-2i)$
$=4i^2 $
$=-4 \qquad [i^2=-1]$
answered Apr 9, 2014 by yamini.v
 

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