Recent content by AlBell

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    Calculating the residue of a complex function

    Ah I forgot about factorising, that makes it so much simpler! I get 3/8 I think!
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    Calculating the residue of a complex function

    Yes but I am having trouble actually implementing the formula and wondered if anyone could do an example to help me understand it?
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    Calculating the residue of a complex function

    I thought it was ?
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    Calculating the residue of a complex function

    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...
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    Are These Quantum States Entangled?

    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...
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    Analyzing Singularities at z=2 & -1/3

    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
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    Analyzing Singularities at z=2 & -1/3

    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...
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    Evaluating Complex Integrals Using Cauchy's Integral Formula

    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?
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    Evaluating Complex Integrals Using Cauchy's Integral Formula

    Can I then use the integral theorem that says it will equal 0?
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    Evaluating Complex Integrals Using Cauchy's Integral Formula

    Ah so the unit circle wouldn't actually contain the point pi/2 whereas the circle mod(z)=2 would?
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    Evaluating Complex Integrals Using Cauchy's Integral Formula

    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...