Engineering Mathematics
Complex Functions
Practice questions from Complex Functions.
33
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IncorrectWhich of the following statements involving contour integrals (evaluated counterclockwise) on the unit circle C in the complex plane is/are TRUE?
, where is an even integer
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Sign in to UnlockLet z be a complex variable. If and C is the circle in the complex plane with __________.
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Sign in to UnlockLet . Which of the following cannot be a value of ?
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Sign in to UnlockThe value of the contour integral,
, where the contour is
, taken in the counter clockwise direction, is
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Sign in to UnlockA simple closed path in the complex plane is shown in the figure. If
where , then the value of is ________ (rounded off to two decimal places).
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Sign in to UnlockConsider the integral
where is a counter-clockwise oriented circle defined as . The value of the integral is
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Sign in to UnlockThe value of the contour integral
Evaluated over the unit circle1 is ________
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Sign in to UnlockWhich one of the following functions is analytic over the entire complex plane?
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Sign in to UnlockThe contour C given below is on the complex plane, where
The value of the integral is ______
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Sign in to UnlockThe residues of a function are ?
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Sign in to UnlockAn integral I over a counterclockwise circle C is given by If C is defined as |z| = 3, then the value of I is
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Sign in to UnlockIn the following integral, the contour C encloses the points 2πj and -2πj.
The value of the integral is_________
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Sign in to UnlockConsider the complex valued function where z is a complex variable. The value of b for which the function f(z) is analytic is _____________.
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Sign in to UnlockFor the residue of the pole at z = 0 is ___________.
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Sign in to UnlockThe values of the integral 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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Sign in to UnlockLet 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?
The residue of at z=1 is ½
(complex conjugate of z) is an analytical function
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Sign in to UnlockIf C denotes the counter clockwise unit circle, the value of the contour integral is _______.
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Sign in to UnlockIf C is a circle of radius r with centre , in the complex z-plane and if n is a non-zero integer, then equals
0
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Sign in to UnlockC is a closed path in the z-plane given by |z| = 3.
The value of the integral is
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Sign in to UnlockThe real part of an analytic function f(z) where is given by . The imaginary part of f(z) is
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Sign in to UnlockGiven , If C is a counter cock wise path in the z-plane such that |z+1|=1,
the value of is
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Sign in to UnlockIf , then the value of is
x
1
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Sign in to UnlockThe value of the integral where c is the circle |z| = 1 is given by
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Sign in to UnlockThe residues of a complex function at its poles are
, and 1
, and -1
, 1 and
, -1 and
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Sign in to UnlockIf then is given by
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Sign in to UnlockThe Taylor series expansion of at is given by
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Sign in to UnlockThe equation sin(z) = 10 has
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Sign in to UnlockWhich of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0?
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Sign in to UnlockThe residue of the function
at z = 2 is
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Sign in to UnlockIn the Taylor series expansion of about the point , the coefficient of is
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Sign in to UnlockIf the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integralis
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Sign in to UnlockFor the function of a complex variable W= lnZ (where, W=u+jv and Z=x+jy), then u=constant lines get mapped in Z-plane as
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Sign in to UnlockThe value of the constant integral in positive sense is
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