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Question
If \[x + iy = \frac{a + ib}{a - ib}\] prove that x2 + y2 = 1.
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Solution
\[x + iy = \frac{a + ib}{a - ib}\]
\[\text { Taking mod on both the sides }: \]
\[\left| x + iy \right| = \left| \frac{a + ib}{a - ib} \right|\]
\[ \Rightarrow \sqrt{x^2 + y^2} = \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}\]
\[ \Rightarrow \sqrt{x^2 + y^2} = 1\]
\[ \Rightarrow x^2 + y^2 = 1\]
\[\text { Hence proved } .\]
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