If x + iy = a+i b a-i b , prove that x^2 + y^2 = 1 - Vidyadip

Question

If x + iy = $\frac{a+i b}{a-i b}$, prove that $x^2 + y^2 = 1$

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Answer

We have $x+i y=\frac{(a+i b)}{(a-i b)}$
=> $|x+i y|=|\frac{(a+i b)}{(a-i b)}|$Squaring Both the sides,
=> $|x + iy|^2 =\frac{|(a+i b)|^2}{|(a-i b)|^2}$
=> $x^2 + y^2 =\frac {a^2 + b^2} {a^2 + b^2}$ = 1

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