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Gate 2021: Engineering Mathematics Quiz 14

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Question 1

Let z be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin, the value of A is

Question 2

For the function  of a complex variable z the point z = 0 is

Question 3

For an analytic function f(x +iy) =u(x,y) +iv(x,y), u is given by u = 3x2 -3y2. The expression for v, considering K to be a constant is?

Question 4

Find the solution for multiplication of two complex no. of the form a+ib and c+id. Take a = 2, b = 3, c = 4 and d = 5.

Question 5

If the conjugate of a complex number is then that complex number is

Question 6

If z is a complex number with modulus 1, such that is not –1, then is
[Assume n is a positive integer]
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