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If ((1-i)/(1+i))^(100)=a+i b ,\ fin d\ (...

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

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Given that , `((1-i)/(1+i))^(100)=a+ib, `
`rArr [(1-i)/(1+i).(1-i)/(1-i)]^(100) = a+ib rArr(((1+i)^(2)-2i)/(1-i^(2)))=a+ib`
`rArr ((-2i)/(2))^(100)=a+ib" "[:.(i^(2)= (-1)] `
`rArr (i)^(25)=a+ib rArr 1=a+ib`
Then, a=1 and b = 0
`:. (a,b)=(1,0)" "[:.(i^(4)=1] `
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