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

$$C$$ is a closed path in the $$z-$$plane given by
$$\left| z \right| = 3.$$ The value of the integral
$$\oint\limits_c {{{{z^2} - z + 4j} \over {z + 2j}}dz} $$ is

The value of the integral $$\oint\limits_c {{{ - 3z + 4} \over {{z^2} + 4z + 5}}} \,\,dz,$$ when $$C$$ is the circle $$|z| = 1$$ is given by

The residues of a complex function $$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}}$$ at it poles