Consider the following series:

$$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$

For which of the following combinations of c, d values does this series converge?

The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are

For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.

The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The imaginary part of $$f(z)$$ is