The residues of a complex function $${\text{X}}\left( {\text{z}} \right) = \frac{{1 - 2{\text{z}}}}{{{\text{z}}\left( {{\text{z}} - 1} \right)\left( {{\text{z}} - 2} \right)}}$$ at its poles are
A. $$\frac{1}{2},\, - \frac{1}{2}{\text{ and }}1$$
B. $$\frac{1}{2},\,\frac{1}{2}{\text{ and }} - 1$$
C. $$\frac{1}{2},\,1{\text{ and }} - \frac{3}{2}$$
D. $$\frac{1}{2},\, - 1{\text{ and }}\frac{3}{2}$$
Answer: Option C
This Question Belongs to Engineering Maths >> Complex Variable
A. -x2 + y2 + constant
B. x2 - y2 + constant
C. x2 + y2 + constant
D. -(x2 + y2) + constant
The product of complex numbers (3 - 2i) and (3 + i4) results in
A. 1 + 6i
B. 9 - 8i
C. 9 + 8i
D. 17 + 6i
If a complex number $${\text{z}} = \frac{{\sqrt 3 }}{2} + {\text{i}}\frac{1}{2}$$ then z4 is
A. $$2\sqrt 2 + 2{\text{i}}$$
B. $$\frac{{ - 1}}{2} + \frac{{{\text{i}}{{\sqrt 3 }^2}}}{2}$$
C. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{2}$$
D. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{8}$$
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