Question

the value of (1+i)^8+(1-i)^8​

Answer 1

Step-by-step explanation:

To find the value of

$( {1 + i)}^{8} + ( {1 - i)}^{8} \\ \\ { {( ({(1 + i)}^{2} })^{2} })^{2} + { {( ({(1 - i)}^{2} })^{2} })^{2} \\ \\ as \: we \: know \: that \\ \\ {a}^{8} = { { ((({a}^{2} })^{2} })^{2} \\ \\ so \\ \\ = > { {( (1 + 2i + {i}^{2} })^{2} })^{2} + { {( (1 - 2i + {i}^{2} })^{2} })^{2} \\ \\ = > { {( (1 + 2i - 1 })^{2} })^{2} + { {( (1 -2 i - 1 })^{2} })^{2} \\ \\ {i}^{2} = - 1 \\ \\ = > { {((2i)}^{2} })^{2} + { {(( - 2i)}^{2} })^{2} \\ \\ = > {(4 {i}^{2} })^{2} + {(4 {i}^{2} })^{2} \\ \\ = > {( - 4)}^{2} + {( - 4)}^{2} \\ \\ = > 16 + 16 \\ \\ = > 32$

Hope it helps you.