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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations3 Marks
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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