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GATE 2019: Engineering Mathematics Test 6

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Question 1

If
 
Where, C: circle , then the value of is

Question 2

A point z has been plotted in the complex plane, as shown in figure below.

The plot of the complex number is

Question 3

Let Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image016.png 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?

Question 4

In the following integral, the contour C enclose the points 2πj and -2πj

The value of the integral is ______

Question 5

The value of contour integral dz over lzl = 1 is

Question 6

Given. If C is a counterclockwise path in the z-plane such that |z + 1| = 1, the value of  is
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Jun 21ESE & GATE EE