Contour Integral of 5z^4+z^3+2: Finding a Square Contour

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In summary, the conversation discusses finding the contour integral of a function in a circle and a square contour. The attempt at a solution involves factoring and identifying poles, but it is noted that the function does not have any poles. The person seeks help with solving the problem.
  • #1
doey
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Homework Statement


given 5z^4+z^3+2

Homework Equations



the question asking me to find the contour integral of thi function in the
C circle of |z|=1. then how about if the Contour is a square with point [0,0][1,0][1,i][0,i] ?

The Attempt at a Solution



i have no idea abt how to do and i attempt to factor up to
z^4[5+ (1/z) +(2/z^4)] and then juz 2∏i(coefficient of 1/z) am i wrong?
and i totally no idea of my pole for the square contour [0,0][1,0][1,i][0,i], anyone pls help me !
 
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  • #2
doey said:

Homework Statement


given 5z^4+z^3+2

Homework Equations



the question asking me to find the contour integral of thi function in the
C circle of |z|=1. then how about if the Contour is a square with point [0,0][1,0][1,i][0,i] ?

The Attempt at a Solution



i have no idea abt how to do and i attempt to factor up to
z^4[5+ (1/z) +(2/z^4)] and then juz 2∏i(coefficient of 1/z) am i wrong?
and i totally no idea of my pole for the square contour [0,0][1,0][1,i][0,i], anyone pls help me !

Your function doesn't have any poles. Does it?
 

Related to Contour Integral of 5z^4+z^3+2: Finding a Square Contour

1. What is a contour integral?

A contour integral is a type of integral used in complex analysis to calculate the total change in a complex-valued function along a given curve or path.

2. How do you find the contour integral of a given function?

To find the contour integral of a given function, you need to first parameterize the contour (or path) and then evaluate the integral using the parameterization.

3. What is a square contour?

A square contour is a type of path or curve that is in the shape of a square. It is often used in complex analysis to simplify the calculation of contour integrals.

4. Can you explain the steps for finding the contour integral of 5z^4+z^3+2 using a square contour?

First, we need to parameterize the square contour. This can be done by setting z as a function of t, where t ranges from 0 to 1. Next, we substitute this parameterization into the given function and evaluate the integral using the fundamental theorem of calculus.

5. Why is finding the contour integral of a given function important?

Finding the contour integral of a function allows us to calculate the total change of a complex-valued function over a given path. This has many applications in physics, engineering, and other fields where complex numbers are used to model real-world phenomena.

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