Test: Complex Variables
15 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Complex Variables
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The integration of f (z) = x2 + ixy from A(1, 1) to B(2, 4) along the straight line AB joining the two points is
x = at + b, y = ct + d
We know by the derivative of an analytic function that
where c is the upper half of the circle z = 1Given contour c is the circle |z| = 1
Let f (z) = cosπz then f(z) is analytic within and on |z| =3, now by Cauchy’s integral formula
around a rectangle with vertices at 
is
where c is the circle x2 + y2 = 4
Que: The value of f(3) is
where c is the circle x2 + y2 = 4
Que: The value of f' (1 - i) is
The point (1 - i) lies within circle |z| = 2 ( ... the distance of 1 - i i.e., (1, 1) from the origin is √2 which is less than 2, the radius of the circle).
Let Ø(z) = 3z2 + 7z + 1 then by Cauchy’s integral formula
Expand the function 
in Laurent’s series for the condition given in question.
Que: 1 < |z| < 2
Expand the function in Laurent’s series for the condition given in question.
Que: |z| > 2
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