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The integration of f (z) = x^{2} + 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
Given 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
where c is the circle x^{2} + y^{2} = 4
Que: The value of f(3) is
where c is the circle x^{2} + y^{2} = 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) = 3z^{2} + 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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