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Question : 20 of 121
Marks:
+1,
-0
Solution:
1+i=√2(cos‌+i‌sin‌) and
‌‌1−i=√2(cos‌−i‌sin‌) ∴‌‌(1+i)8+(1−i)8=24(cos‌+i‌sin‌)8 +24(cos‌−i‌sin‌) =‌‌24(cos‌2‌π+i‌sin‌2‌π)+24(cos‌2‌π−i‌sin‌2‌π) [∵(cos‌θ+i‌sin‌θ)n=cos‌n‌θ+i‌sin‌n‌θ] =‌‌24(2‌cos‌2‌π)=25
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