If $$C$$ is a circle of radius $$r$$ with centre $${z_0}$$ in the complex $$z$$-plane and if $$'n'$$ is a non-zero integer, then $$\oint\limits_c {{{dz} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}} $$ equals

Let $$f\left( z \right) = {{az + b} \over {cz + d}}.$$ If $$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$ for all $${z_1} \ne {z_2}.\,\,a = 2,\,\,b = 4$$ and $$C=5,$$ then $$d$$ should be equal to

If $$C$$ denotes the counter clockwise unit circle. The value of the contour integral $${1 \over {2\pi i}}\oint\limits_c {{\mathop{\rm Re}\nolimits} \left\{ z \right\}dz} $$ is __________.

Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction . Which one of the following statement is NOT TRUE?