Homework Statement
calculate the residue of the pole at z=i of the function
f(z)=(1+z^2)^-3
State the order of the pole
Homework Equations
I know the residue theorem and also the laurent series expansion but I'm having trouble applying these
The Attempt at a Solution
I...
Homework Statement
I've been asked to find out if are entangled states or not
Homework Equations
I thought an entangled state was one where a measurement of one qubit revealed the nature of the other qubit in the state
The Attempt at a Solution
If I am correct in my definition of an...
I know I don't have to but I thought that a laurent expansion was another way to find out the nature of a singularity, like what the order of the pole was, and I just wanted to try and get a grasp of this technique as well and get the same answer for both techniques
Homework Statement
I have been asked to state the precise nature of the singularities at z=2 and z=-1/3 in
Homework Equations
I know the laurent series is given by
The Attempt at a Solution
I think I need to expand the series out into a laurent series around z=2 and z=-1/3 but...
I'm a bit confused again, sorry!
I thought that the z-Pi/2 on the denominator of the integral means we just shift the origin of the circle to a new position?
Homework Statement
Use Cauchy's integral formula to evaluate when
a) C is the unit circle
b) c is the circle mod(Z)=2
Homework Equations
I know the integral formula is
The Attempt at a Solution
for the unit circle I was attempting F(z)=sin(z) and Z0=∏/2, which would give a...