• # question_answer The value of ${{(1+i)}^{8}}+{{(1-i)}^{8}}$ is  [RPET 2001; KCET  2001] A) 16 B) - 16 C) 32 D) - 32

$\because \,{{(1+i)}^{2}}=\,1+{{i}^{2}}+2i=2i$ and ${{(1-i)}^{2}}=1+{{i}^{2}}-2i=-2i$ $\Rightarrow {{(1+i)}^{8}}+{{(1-i)}^{8}}={{(2i)}^{4}}+{{(-2i)}^{4}}$$={{2}^{4}}({{i}^{4}}+{{i}^{4}})$                             $={{2}^{5}}=32.$