residue theorem

If C is the unit circle in the complex plane with its center at the origin, then the value of n in the equation given below is ________ (rounded off to 1 decimal place). $\oint_C \...

The value of the integral $\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$ evaluated over a counter-clockwise circular contour in the complex plane enclosing o...

Let z be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin, $\oint_C \frac{1}{5z-4} dz = A\pi i$, the value of A is

The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$ evaluated using contour integration and the residue theorem is

The integral $$\oint {f(z)dz} $$ evaluated around the unit circle on the complex plane for $$f(z) = {{\cos z} \over z}$$ is