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# GATE 2022 : Engineering Mathematics - Complex Variables - 1

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Question 1

Let where z is a complex number not equal to zero. Then z is solution of

Question 2

Assuming i=√-1 and t is a real number, is _________.

Question 3

Consider the complex valued function where z is a complex variable. The value of b for which the function f(z) is analytic is

Question 4

The contour given below is on the complex plane where  The value of the integral is __________.

Question 5

The integral is evaluated along the real axis from 0 to 2 and vertically upward to (2 + i). If I = A + Bt, then value of A will be______

(Assume is the complex conjugate of z)

Question 6

Let f(z) = (x2+y2) + i2xy and g(z) = 2xy + i(y2–x2) for z = x+iy where . Then in the complex plane C.
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