Engineering Mathematics
Complex Functions
Practice questions from Complex Functions.
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IncorrectLet 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).
Method-1
Given:
(-ve sign as contour is in clockwise direction, which is negative direction of angle)
Method-2
No poles of exist inside the contour
is an analytic function inside the contour .
By Cauchy Integral Theorem
Which of the following complex functions is/are analytic on the complex plane?
Analytic functions don’t contain
or simplification.
Option D –
By Cauchy Riemann Equations
Since,
Cauchy Riemann Equations are satisfied so function is analytic.
Consider the complex function . The coefficient of in the Taylor series expansion of about the origin is ________ (rounded off to 1 decimal place).
Expanding the given function with the help of Taylor Series
no term present
