Complex Variable MCQs Question and Answer in Engineering Maths

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If n is a positive integer then, (√3 + i)ⁿ + (√3 - i)ⁿ is

A) $${2^{\text{n}}}\sin \frac{{{\text{n}}\pi }}{6}$$ B) $${2^{\text{n}}}\cos \frac{{{\text{n}}\pi }}{6}$$ C) $${2^{{\text{n}} + 1}}\cos \frac{{{\text{n}}\pi }}{6}$$ D) $${2^{{\text{n}} + 1}}\sin \frac{{{\text{n}}\pi }}{6}$$

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Answer: Option C

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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?

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Answer & Solution

Answer: Option B

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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

A) -πi B) 0 C) πi D) 2πi

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Answer & Solution

Answer: Option C

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If z is a complex variable, the value of $$\int\limits_5^{3{\text{i}}} {\frac{{{\text{dz}}}}{{\text{z}}}} $$ is

A) -0.511 - 1.57i B) -0.511 + 1.57i C) 0.511 - 1.57i D) 0.511 + 1.57i

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Answer & Solution

Answer: Option B

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For the function $$\frac{{\sin {\text{z}}}}{{{{\text{z}}^3}}}$$ of a complex variable the point z = 0 is

A) a pole of order 3 B) a pole of order 2 C) a pole of order 1 D) not a singularity

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Answer & Solution

Answer: Option B

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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

A) $$\frac{2}{5}$$ B) $$\frac{1}{2}$$ C) 2 D) $$\frac{4}{5}$$

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Answer & Solution

Answer: Option A

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Let $${\text{j}} = \sqrt { - 1} .$$ Then one value of j^j is

A) √j B) -1 C) $$\frac{\pi }{2}$$ D) $${{\text{e}}^{ - \frac{\pi }{2}}}$$

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Answer & Solution

Answer: Option D

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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

A) -8 B) -4 C) 0 D) 4

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Answer & Solution

Answer: Option C

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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

A) 0 B) $$\frac{1}{{10}}$$ C) $$\frac{4}{5}$$ D) 1

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Answer & Solution

Answer: Option A

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The value of $$\oint\limits_{\text{C}} {\frac{{{\text{dz}}}}{{\left( {1 + {{\text{z}}^2}} \right)}}} $$ where C is the contour |z - i/2| = 1 is

A) 2πi B) π C) tan^-1z D) πi tan^-1z

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Answer & Solution

Answer: Option B

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