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

prove that :  x2 + y2 = 1

From these equations, we get

x = ±y

when x = y then x = y =  

when x = –y then xy = 1/2 ⇒ –y2 = 1/2 ⇒ y = i , but x and y are not imaginary numbers.

 x2 + y2 =  

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