If $\tan ^{-1}(\alpha+i \beta)=x+i y$, then $x$ is equal to

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

\tan ^{-1}(\alpha+i \beta)=x+i y

, then

x

is equal to

View answer and explanation

Correct option: B

\frac{1}{2} \tan ^{-1}\left(\frac{2 \alpha}{1+\alpha^2+\beta^2}\right)

Option A (

\frac{1}{2} \tan ^{-1}\left(\frac{2 \alpha}{1-\alpha^2-\beta^2}\right)

) is correct because using the tangent addition formula and taking the real part leads to the correct expression for

x

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