If C is a circle |z| = 4 and then is
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Engineering Maths · all questionsComplex Variable
Complex Variable
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What is the residue of the function at its pole?
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Let z = x + jy where Then
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Consider the function f(z) = z + z∗ where z is a complex variable and z∗ denotes its complex conjugate. Which one of the following is TRUE?
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Consider the analytic function f(z) = x2 - y2 + i2xy of the complex variable z = x + iy, where The derivative f'(z) is
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Using Cauchy's integral theorem, the value of the integral (integration being taken in counterclockwise direction) is
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The value of the integral (where C is a closed curve given by |z| = 1) is
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If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral is
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A harmonic function is analytic if it satisfies the Laplace equation. If u(x, y) = 2x2 - 2y2 + 4xy is a harmonic function, then its conjugate harmonic function v(x, y) is
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The complex function tan h(s) is analytic over a region of the imaginary axis of the complex s-plane if the following is TRUE everywhere in the region for all integers n
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Let f1(z) = z2 and f2(z) = be two complex variable function. Here is the complex conjugate of z. Choose the correct answer.
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If represents the complex potential for an electric field. Given then the function is
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An integral over a counter-clockwise circle C is given by
If C is defined as |z| = 3, then the value of is
If C is defined as |z| = 3, then the value of is
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The function is singular at
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If f(z) has a pole of order n at z = a, then Residue of function f(z) at a is
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Which one of the following functions is analytic over the entire complex plane?
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Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
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An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y), where If u(x, y) = 2xy, then v(x, y) must be
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Polar form of the Cauchy-Reimann equations is
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Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz∗ where z∗ denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane
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