Engineering Maths · all questions

Complex Variable
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Q41

Open question

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

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Q42

Open question

A complex variable Z = x + j0.1 has its real part x varying in the range

- \infty

+ \infty

. Which one of the following is the locus (shown in thick lines) of 1/Z in the complex plane?

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Q43

Open question

Integration of the complex function

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

in the counterclockwise direction, around |z - 1| = 1, is

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Q44

Open question

If z is a complex variable, the value of

5 \int 3 i \frac{dz}{z}

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Q45

Open question

For the function

\frac{sin z}{z ^{3}}

of a complex variable the point z = 0 is

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Q46

Open question

Let z be a complex variable. For a counterclockwise integration around a unit circle C, centered at origin.

\oint_{c} \frac{1}{5 z - 4} dz = A π i

the value of A is

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Q47

Open question

Let

j = - 1 .

Then one value of j^j is

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Q48

Open question

The sum of residues of

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

at its singular point is

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Q49

Open question

The value of the Integral

c \oint \frac{- 3 z + 4}{( z ^{2} + 4 z + 5 )} dz

where c is the circle |z| = 1 is given by

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Q50

Open question

The value of

C \oint \frac{dz}{( 1 + z ^{2} )}

where C is the contour |z - i/2| = 1 is

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Q51

Open question

The value of the integral

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

in counter clockwise direction around a circle C of radius 1 with center at the point z = -2 is

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Q52

Open question

The integral

\oint f (z) dz

evaluated around the unit circle on the complex plane for

f (z) = \frac{cos z}{z}

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Q53

Open question

The residues of a function

f (z) = \frac{1}{( z - 4 ) ( z + 1 ) ^{3}}

are

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Q54

Open question

The value of expression

\frac{- 5 + i 10}{3 + 4 i}

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Q55

Open question

The argument of the complex number

\frac{1 + i}{1 - i},

where

i = - 1,

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Q56

Open question

The nature of singularity of function

f (z) = \frac{1}{cos z - sin z}

z = \frac{π}{4}

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Q57

Open question

A point z has been plotted in the complex plane, as shown in figure below.
Complex Variable mcq question image

The plot for point

\frac{1}{z}

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Q58

Open question

The analytic function

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

has singularities at

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Q59

Open question

The values of the integral

\frac{1}{2 π j} c \oint \frac{e ^{z}}{z - 2} dz

along a closed contour c in anti-clockwise direction for
i. the point z₀ = 2 inside the contour c, and
ii. the point z₀ = 2 outside the contour c, respectively, are

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Q60

Open question

Evaluate:

c \int \frac{dz}{z sin z},

where c is x² + y² = 1.

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Complex Variablepractice.

Complex Variable
practice.