Complex Variable MCQs with Answers 2027

Q1

f(z) = u(x, y) + iv(x, y) is an analytic function or complex variable z = x + iy where

i = - 1,

u(x, y) = 2xy, then v(x, y) may be expressed as

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Q2

Open question

The product of complex numbers (3 - 2i) and (3 + i4) results in

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Q3

Open question

If a complex number

z = \frac{3}{2} + i \frac{1}{2}

then z⁴ is

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Q4

Open question

If C is a circle of radius r with centre z₀, in the complex z-plane and if n is a non-zero integer, then

\oint \frac{dz}{( z - z _{0} ) ^{n + 1}}

equals

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Q5

Open question

Contour C in the adjoining figure is described by x² + y² = 16. The value

c \oint \frac{z ^{2} + 8}{0.5 z - 1.5 j} dz

is (Note:

j = - 1

)

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Q6

Open question

The value of

\oint \frac{sin z}{z} dz,

where the counter of integration is a simple closed curve around the origin, is

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Q7

Open question

z = \frac{2 - 3 j}{- 5 + i}

can be expressed as

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Q8

Open question

Consider the following complex function

f (z) = \frac{9}{( z - 1 ) ( z + 2 ) ^{2}}

Which of the following is one of the residues of the above function?

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Q9

Open question

The value of

c \oint \frac{z ^{2}}{z ^{4} - 1} dz

using Cauchy's integral formula, around circle |z + 1| = 1 where z = x + iy is

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Q10

Open question

The modulus of the complex number

(\frac{3 + 4 i}{1 - 2 i})

is

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Q11

Open question

If f(z) = (x² + ay²) + i bxy is a complex analytic function of z = x + iy, where

i = - 1,

then

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Q12

Open question

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y) where

i = - 1 .

If u = xy, the expression for v should be

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Q13

Open question

F(z) is a function of the complex variable z = x + iy given by F(z) = iz + k Re(z) + i

I

m(z)
For what value of k will F(z) satisfy the Cauchy-Riemann equations

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Q14

Open question

The value of the integral

- \infty \int \infty \frac{sin x}{x ^{2} + 2 x + 2} dx

evaluated using contour integration and the residue theorem is

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Q15

Open question

Consider the line integral

I = \int_{c} (x^{2} + i y^{2}) dz,

where z = x + iy. The line c is shown in the figure below
Complex Variable mcq question image

The value of

I

is

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Q16

Open question

The product of a complex number z = x + iy and its complex conjugate

z

is

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Q17

Open question

If z = x + jy, where x and y are real, the value of |e^jz| is

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Q18

Open question

The value of

\oint \frac{1}{z ^{2}} dz,

where the contour is the unit circle traversed clockwise, is

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Q19

Open question

Evaluate

\oint_{c} \frac{1}{( z - 1 ) ^{3} \cdot ( z - 3 )} dz

where c is the rectangular region defined by x = 0, x = 4, y = -1 and y = 1

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Q20

Open question

If f(z) = C₀ + C₁z^-1, then

unit circle \oint \frac{1 + f ( z )}{z} dz

is given by

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