If `((1-i)/(1+i))^(100)=a+i b , fin d (a , b)` – InterviewSolution

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1.	If `((1-i)/(1+i))^(100)=a+i b , fin d (a , b)`
Answer» Correct Answer - `a = 1, b = 0` `((1-i))/((1+i))=((1-i))/((1+i))xx((1-i))/((1-i))=((1-i)^(2))/(2)=((1+i^(2)-2i))/(2)= -i`. `therefore" "((1-i)/(1+i))^(100)=(-i)^(100) ={(-i)^(4)}^(25)=(1)^(25)=1" "[because (-i)^(4) = i^(4) = 1]`. Hence, a = 1 and b = 0.

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