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Question: Find real part of \(\tan^{- 1}(1 + i)\)...

Find real part of tan⁡−1(1+i)\tan^{- 1}(1 + i)

A

−12tan⁡−1- \frac{1}{2}\tan^{- 1}{}

B

12tan⁡−1(2)\frac{1}{2}\tan^{- 1}(2)

C

−12tan⁡−1(12)- \frac{1}{2}\tan^{- 1}\left( \frac{1}{2} \right)

D

0

Answer

−12tan⁡−1- \frac{1}{2}\tan^{- 1}{}

Explanation

Solution

Real part = 12tan⁡−12(1)1−1−1=−12tan⁡−1(2)\frac{1}{2}\tan^{- 1}\frac{2(1)}{1 - 1 - 1} = - \frac{1}{2}\tan^{- 1}(2).