Inverse Trigonometry of Complex Numbers? Really?

Calculus Level 5

\[\large{\begin{cases} P = \dfrac{\tan^{-1}(\alpha)}{\alpha} + \dfrac{\tan^{-1}(\beta)}{\beta} + \dfrac{\tan^{-1}(\gamma)}{\gamma} \\ \text{ . } \\ \text{ . } \\ Q = \displaystyle \sum_{n=0}^\infty \dfrac{(-1)^n}{6n+1} \end{cases} }\]

If \(\alpha, \ \beta, \ \gamma \) are the three cube roots of unity, submit the value of \(\dfrac{P}{Q}\) as your answer.

×

Problem Loading...

Note Loading...

Set Loading...