Question

. If x + iy =
√1 + i
√1 - i
prove that x2 + y2 = 1.​

Answer 1

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Answer 2

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 = 1