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Question
If \[\frac{( a^2 + 1 )^2}{2a - i} = x + iy, \text { then } x^2 + y^2\] is equal to
Options
\[\frac{( a^2 + 1 )^4}{4 a^2 + 1}\]
\[\frac{(a + 1 )^2}{4 a^2 + 1}\]
\[\frac{( a^2 - 1 )^2}{(4 a^2 - 1 )^2}\]
none of these
Solution
\[\frac{( a^2 + 1 )^4}{4 a^2 + 1}\]
\[x + iy = \frac{\left( a^2 + 1 \right)^2}{2a - i}\]
Taking modulus on both the sides, we get:
\[\text { Squaring both sides, we get,} \]
\[ x^2 + y^2 = \frac{\left( a^2 + 1 \right)^4}{4 a^2 + 1}\]
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