Engineering Mathematics
Complex Functions
Practice questions from Complex Functions.
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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
Exponential, Sinusoidal and Polynomials in z are always analytic over entire z-plane
For analytic functions the integral over closed contour is always 0.
(i) is always analytic function
(i) is always analytic function
(ii) even integer is always analytic function
(iii) is also analytic function in contour .
(iv)
Poles:
Hence, no poles of lies in contour . Thus, is analytic in contour .
Hence, option (A) am (B) are correct.
Let z be a complex variable. If and C is the circle in the complex plane with __________.
Residue at [double pole]
Residue at z=2 (single pole)
By Residue Theorem
Let . Which of the following cannot be a value of ?
Given equation is
On expanding the equation we get.
For
For
For
Option (a) is not Correct.
The value of the contour integral,
, where the contour is
, taken in the counter clockwise direction, is
Let the contour integral,
The given denominator equation can be written as
Poles are given
Only one poll is inside other is outside.
where lies outside ''
by Cauchy's residue theorem,
