prove that

Asked by  | 19th Jul, 2008, 06:37: PM

Expert Answer:

let z= x+iy

then x2+y2=1  since | z |=1

z-1=(x-1)+iy

z+1=(x+1)+iy

real of (z-1)/(z+1) =  (  (x-1)*(x+1) +y2  ) /  (   (x+1)2+y2  )   ( bu multipling complex conjugate of  (z+1) to numerator and denominator  )

numerator of this real part is x2+y2-1 which is zero so (z-1)/(z+1) is purely imaginary.

Answered by  | 10th Aug, 2008, 04:54: PM

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