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Question

If tan-1α+iβ=x+iy then x=


A

12tan-12α1-α2-β2

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B

12tan-12α1+α2+β2

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C

tan-12α1-α2-β2

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D

None of these

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Solution

The correct option is A

12tan-12α1-α2-β2


Explanation for the correct option:

Given information:

tan-1α+iβ=x+iy …(1)

Write the conjugate and solve

tan-1α-iβ=x-iy …(2)

Add equations (1) and (2)

x+iy+x-iy=tan-1α+iβ+tan-1α-iβ

2x=tan-1α+iβ+tan-1α-iβx=12tan-1α+iβ+α-iβ1-α+iβα-iβx=12tan-12α1-α2-β2

Hence option (A) is correct.


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