Question

If \[\frac{1 - ix}{1 + ix} = a + ib\] then \[a^2 + b^2\]

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Answer 1

1

\[\frac{1 - ix}{1 + ix} = a + ib\]

\[\text { Taking modulus on both the sides, we get }: \]

\[\left| \frac{1 - ix}{1 + ix} \right| = \left| a + ib \right|\]

\[ \Rightarrow \frac{\sqrt{1^2 + x^2}}{\sqrt{1^2 + x^2}} = \sqrt{a^2 + b^2}\]

\[ \Rightarrow \sqrt{a^2 + b^2} = 1\]

\[\text { Squaring both the sides, we get: } \]

\[ a^2 + b^2 = 1\]