- Thread starter
- #1
- Jan 17, 2013
- 1,667
Do we have identities for the following
\(\displaystyle \arctan(x+y) = \)
\(\displaystyle \arctan(x)-\arctan(y) = \)
\(\displaystyle \arctan(x+y) = \)
\(\displaystyle \arctan(x)-\arctan(y) = \)
\(\displaystyle \displaystyle \begin{align*} \arctan{(z)} &= \frac{i}{2} \ln {\left( \frac{i + z}{i - z} \right) } \\ &= \frac{i}{2} \left[ \ln{ \left| \frac{i + z}{i - z} \right| } + i \arg{ \left( \frac{i + z}{i - z} \right) } \right] \\ &= -\frac{1}{2}\arg{ \left( \frac{i + z}{i - z} \right) } + i \left( \frac{1}{2} \ln{ \left| \frac{i + z}{i - z} \right| } \right) \end{align*}\)I am looking for the real and imaginary part of
$$\arctan(x+iy) $$
For $|z|<1$ is...I am looking for the real and imaginary part of
$$\arctan(x+iy) $$