Engineering Mathematics
Complex Functions
Practice questions from Complex Functions.
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IncorrectThe magnitude of the contour integral
over the contour is
(Round off to two decimal places)
Note: is a complex variable and
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Sign in to UnlockLet be a clockwise oriented closed curve in the complex plane defined by . Further, let be a complex function, where . Then, __________ (round off to the nearest integer).
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Sign in to UnlockWhich of the following complex functions is/are analytic on the complex plane?
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Sign in to UnlockConsider the complex function . The coefficient of in the Taylor series expansion of about the origin is ________ (rounded off to 1 decimal place).
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Sign in to UnlockLet , where is a complex number. Which one of the following is true?
The complex roots of the equation come in conjugate pairs.
All the roots cannot be real.
The sum of the roots of is real number
Conjugate conjugate for all
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Sign in to UnlockLet and be the vertices of rectangle in the complex plane. Assuming that is traversed in counter-clockwise direction, the value of the contour integral is
0
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Sign in to UnlockThe value of the following complex integral, with representing the unit circle centered at origin in the counterclockwise sense, is
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Sign in to UnlockWhich one of the following functions is analytic in the region ?
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Sign in to UnlockThe closed loop line integral
evaluated counter-clockwise, is
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Sign in to UnlockThe value of the integral in counter clockwise direction around a circle C of radius 1 with centre at the point Z= -2 is
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Sign in to UnlockIf C is a circle and , then is
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Sign in to UnlockFor a complex number
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Sign in to UnlockConsider the line integral The line c is shown in the figure below
The value of I is
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Sign in to UnlockThe value of the contour integral in the complex-plane . Along the contour , taken counter-clockwise is
0
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Sign in to UnlockThe value of the integral , over the contour, taken in the anti – clockwise direction, would be
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Sign in to UnlockConsider the function where z is a complex variable and denotes it complex conjugate. Which one of the following is TRUE?
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Sign in to UnlockLet be the set of points in the complex plane corresponding to the unit circle: . Consider the function where denotes the complex conjugate of . The f(z) maps S to which one of the following in the complex plane.
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Sign in to UnlockAll the values of the multi – valued complex function , where , are
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Sign in to UnlockIntegration of the complex function, in the counterclockwise direction, around, is
0
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Sign in to UnlockSquare roots of –i, where
i, –i
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Sign in to UnlockEvaluated anticlockwise around the circle, where i =, is
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Sign in to UnlockIf , then the value of is
x
1
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Sign in to UnlockGiven. If C is a counter clockwise path in the z-plane such that, the value of is
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Sign in to UnlockA point z has been plotted in the complex plane, as shown in figure below.
The plot of the complex number is
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Sign in to UnlockThe value of where C is the contour is
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