# Evaluate (1+i)^8 +(1-i)^9 =?

Solution:   Given ,$\left ( 1+i \right )^{8}+\left ( 1-i \right )^{9}$

$\\ \\ \Rightarrow \hspace{1cm} [(1+i)^{2}]^{4}+[(1-i)^{2}]^{4}(1-i)\\ \\ \Rightarrow \hspace{1cm}(2i)^{4}+(-2i)^{4}(1-i)\\ \\ \Rightarrow \hspace{1cm}16+16(1-i)=16(2-i)=32-16i$

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