21. If C is a circle |z| = 4 and $${\text{f}}\left( {\text{z}} \right) = \frac{{{{\text{z}}^2}}}{{{{\left( {{{\text{z}}^2} - 3{\text{z}} + 2} \right)}^2}}},$$ then $$\oint\limits_{\text{c}} {{\text{f}}\left( {\text{z}} \right){\text{dz}}} $$ is
22. What is the residue of the function $$\frac{{1 - {{\text{e}}^{2{\text{z}}}}}}{{{{\text{z}}^4}}}$$ at its pole?
23. Let z = x + jy where $${\text{j}} = \sqrt { - 1} .$$ Then $$\overline {\cos {\text{z}}} = ?$$
24. Consider the function f(z) = z + z∗ where z is a complex variable and z∗ denotes its complex conjugate. Which one of the following is TRUE?
25. Consider the analytic function f(z) = x2 - y2 + i2xy of the complex variable z = x + iy, where $${\text{i}} = \sqrt { - 1} .$$ The derivative f'(z) is
26. Using Cauchy's integral theorem, the value of the integral (integration being taken in counterclockwise direction) $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^3} - 6}}{{3{\text{z}} - {\text{i}}}}{\text{dz}}} $$ is
27. The value of the integral $$\int\limits_{\text{c}} {\frac{{\cos \left( {2\pi {\text{z}}} \right)}}{{\left( {2{\text{z}} - 1} \right)\left( {{\text{z}} - 3} \right)}}{\text{dz}}} $$ (where C is a closed curve given by |z| = 1) is
28. If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral $$\oint\limits_{\text{D}} {\frac{1}{{\left( {{{\text{s}}^2} - 1} \right)}}{\text{ds}}} $$ is
