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Mathematics · JEE | COMPLEX NUMBERS AND QUADRATIC EQUATIONS
हिन्दीIf \( x + iy = \frac{a + ib}{a - ib} \), then the value of \( x^2 + y^2 \) is:
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Correct answer · Option C
\( 1 \)
Explanation
Taking modulus on both sides, \( |x + iy| = \left|\frac{a + ib}{a - ib}\right| \). Since \( |a + ib| = |a - ib| = \sqrt{a^2 + b^2} \), we get \( \sqrt{x^2 + y^2} = 1 \implies x^2 + y^2 = 1 \).
