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

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

48.
The sum of residues of $${\text{f}}\left( {\text{z}} \right) = \frac{{2{\text{z}}}}{{{{\left( {{\text{z}} - 1} \right)}^2}\left( {{\text{z}} - 2} \right)}}$$    at its singular point is

49.
The value of the Integral $$\oint\limits_{\text{c}} {\frac{{ - 3{\text{z}} + 4}}{{\left( {{{\text{z}}^2} + 4{\text{z}} + 5} \right)}}{\text{dz}}} $$    where c is the circle |z| = 1 is given by