41. If n is a positive integer then, (√3 + i)n + (√3 - i)n is
42. A complex variable Z = x + j0.1 has its real part x varying in the range $$ - \infty $$ to $$ + \infty $$ . Which one of the following is the locus (shown in thick lines) of 1/Z in the complex plane?
43. Integration of the complex function $${\text{f}}\left( {\text{z}} \right) = \frac{{{{\text{z}}^2}}}{{{{\text{z}}^2} - 1}},$$ in the counterclockwise direction, around |z - 1| = 1, is
44. If z is a complex variable, the value of $$\int\limits_5^{3{\text{i}}} {\frac{{{\text{dz}}}}{{\text{z}}}} $$ is
45. For the function $$\frac{{\sin {\text{z}}}}{{{{\text{z}}^3}}}$$ of a complex variable the point z = 0 is
46. Let z be a complex variable. For a counterclockwise integration around a unit circle C, centered at origin.
$$\oint_{\text{c}} {\frac{1}{{5{\text{z}} - 4}}{\text{dz}}} = {\text{A}}\pi {\text{i}}$$ the value of A is
$$\oint_{\text{c}} {\frac{1}{{5{\text{z}} - 4}}{\text{dz}}} = {\text{A}}\pi {\text{i}}$$ the value of A is