If (x + iy) = sqrt [(1+i)/(1-i)],

prove that : x^{2} + y^{2} = 1

From these equations, we get

*x = ±y*

when *x* = *y* then *x* = *y = *

when *x* = –*y *then* xy *= 1/2 ⇒ –*y ^{2} *= 1/2 ⇒

*y*= i , but

*x*and

*y*are not imaginary numbers.

* *∴ *x*^{2} + *y*^{2} =

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