If I turn everything into z-∏, do we need to use the same method as I used to work out z=0 and z=\frac{∏}{2}?
But how? Turn the limit to z-∏→0?
Because I used computer to work out the answer of z=∏ which is -1. But I still cannot get this answer by myself.
Homework Statement
Find the residues of the function
Homework Equations
f(z)=\frac{1}{sin(z)} at z=0, \frac{∏}{2}, ∏
The Attempt at a Solution
Since the function has a simple pole at z=0
I used: Res(f,0)=lim_{z->0}(z-0)\cdot\frac{1}{sin(z)}=1. This means the residue of the function at z=0...
Homework Statement
To find the integral by Cauchy Residue Theorem and apply substitution method.
Homework Equations
To show: ∫^{2∏}_{0}\frac{cosθ}{13+12cosθ}=-\frac{4∏}{15}
The Attempt at a Solution
The solution I have done is attached. It is different as what the question wants me...
Homework Statement
To find entire functions which satisfy g(\frac{1}{n}) = g(-\frac{1}{n}) = \frac{1}{n^{2}}
Homework Equations
How many functions can be found?
The Attempt at a Solution
Because the function is entire, it can be expanded in the Taylor series. But how can I work out the...
Homework Statement
The question is needed to be done by using an appropriate substitution and the Cauchy Integral Formula.
Homework Equations
Evaluate the complex integral: ∫e^(e^it) dt, from 0 to 2∏
The Attempt at a Solution
I cannot find an appropriate substitution for the integral.