Can anyone help me finding the real and the imaginary part of the function $f(x)=\cot(x+i)$, where $i=\sqrt{-1}$?
EDIT: $x\in \mathbb R$.
Can anyone help me finding the real and the imaginary part of the function $f(x)=\cot(x+i)$, where $i=\sqrt{-1}$?
EDIT: $x\in \mathbb R$.
If $x\in \mathbb R$, then you should be able to use the definition of complex sine and cosine, and then multiply both the numerator and denominator by the complex conjugate.
$\begin{align*}\cot(x+i) &= \frac{\cos(x+i)}{\sin(x+i)}\\ &=\frac{\cos x \cosh 1 -i\sin x \sinh 1}{\sin x \cosh 1 + i \cos x \sinh 1}\end{align*}$ ... and so on. Related: http://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_and_complex_numbers