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ESE 2020: Engg. Mathematics Quiz 4
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Question 1
The real part of the complex number
is:
is:
Question 2
Given f(z) = g(z) + h(z) where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE?
Question 3
Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = l}). Consider the function f(z)=zz* where z* denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane
Question 4
Consider the function f(z) = z + z* where z is a complex variable and z* denotes its complex
conjugate. Which one of the following is true?
conjugate. Which one of the following is true?
Question 5
The value of the contour integral in the complex-plane
Along the contour |Z| = 3, taken counter-clockwise is
Along the contour |Z| = 3, taken counter-clockwise is
Question 6
If the conjugate of a complex number is 
then that complex number is
then that complex number is Question 7
In the complex plane, the angle between line (1 + i) and (-1 + i) is ____degrees.
(where, (
)
(where, (
)Question 8
The infinite series 
corresponds to
corresponds to Question 9
An analytic function of a complex variable 
is expressed as 
where 
If
then expression for 
in terms of x, y and a general constant c would be
is expressed as where If
then expression for in terms of x, y and a general constant c would be Question 10
An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x, y). Then, u(x, y) and v(x, y) must satisfy
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Apr 20ESE & GATE CE
