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Evaluate : $\; (1+i)^{6} +(1-i)^{3}$

$\begin{array}{1 1} 0 \\ 2-5i \\ 2+10 i \\ -2-10i \end{array} $

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Answer : $\;-2-10i$
Explanation :
$\; (1+i)^{6} = ((1+i)^{2})^{3}$
$= (1^{2} + i^{2} + 2i )^{3}$
$= (1-1+2i)^{3} = 8i^{3} = -8 i$
$(1-i)^{3} = 1^{3} - i^{3} -3i + 3i^{2}$
$= 1 + i -3i -3 = -2-2i$
$\; (1+i)^{6} +(1-i)^{3} = -8i -2-2i$
$=-2-10i\;.$
answered Apr 17, 2014 by yamini.v
 

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