If ^ -1 ( +i )=x+iy, then x = [RPET 2002] - Vidyadip

MCQ

If ${{\tan }^{-1}}(\alpha +i\beta )=x+iy,$ then x = [RPET 2002]

✓
$\frac{1}{2}{{\tan }^{-1}}\left( \frac{2\alpha }{1-{{\alpha }^{2}}-{{\beta }^{2}}} \right)$
B
$\frac{1}{2}{{\tan }^{-1}}\left( \frac{2\alpha }{1+{{\alpha }^{2}}+{{\beta }^{2}}} \right)$
C
${{\tan }^{-1}}\left( \frac{2\alpha }{1-{{\alpha }^{2}}-{{\beta }^{2}}} \right)$
D
None of these

✓

Answer

Correct option: A.

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

A

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