engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Complex Variables Residue Theorem
Consider the integral \(\mathop \smallint \nolimits_C f\left( x \right)dx,\;f\left( x \right) = \frac{{z - 8}}{{z\left( {z - 4} \right)}}\;\)
Where C is the circle of radius 7, center at the origin.
Which of the following is/are true?
1
f(z) has 2 simple poles and one zero
2
The residue of f(z) at z = 0 is 2
3
The residue at f(z) at z = 4 is 1
4
The value of the integral is 6πi