GATE ME Complex variables PYQs & Answers — Page 2

Questions 11–16 of 16. Imported answers require independent review unless marked reviewed.

Topic practice 16 questionsPage 2 of 2

An analytic function of a complex variable z = x + iy (i = √−1) is defined as

where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is ______ (round off to 2 decimal places).

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An analytic function

of complex variable

may be written as

. Then,

and

must satisfy

Your answerChoose one option.

and

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A harmonic function is analytic if it satisfies the Laplace equation. If

is a harmonic function, then its conjugate harmonic function

Your answerChoose one option.

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

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

Your answerChoose one option.

−1

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Let

be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin,

the value of A is

Your answerChoose one option.

2/5

1/2

4/5

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is a complex analytic function of

, where

, then

Your answerChoose one option.

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GATE ME Complex variables PYQs