Evaluating Complex Integration I_c |z^2|

In summary, complex integration is a mathematical technique used to calculate the integral of complex-valued functions over a given path. It is an extension of regular integration and involves integrating a complex-valued function over a path in the complex plane. Evaluating complex integration I_c |z^2| is important in solving problems in various fields such as physics, engineering, and mathematics. Some common techniques used to evaluate complex integration I_c |z^2| include using the Cauchy integral formula, the residue theorem, and contour integration. It is important in science because many physical and mathematical problems involve complex functions and require calculating complex integrals.
  • #1
AkilMAI
77
0
How can I evaluate I_c |z^2|,where I is the integral and c is the square with vertices at (0, 0), (1, 0), (1, 1), (0, 1) traversed anti-clockwise...?
 
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  • #2
Did you write a parametrization of this square?
 
  • #3
how will that help?
 
  • #4
It's needed to compute a path integral.
 
  • #5
ok ...how should I proceed?
 
  • #6
James said:
ok ...how should I proceed?

What would be the equation of the four lines that make the square, and between which values are these lines defined?
 
  • #7
max(x^2,y^2) with sides of 1?
 

FAQ: Evaluating Complex Integration I_c |z^2|

What is complex integration?

Complex integration is a mathematical technique used to calculate the integral of complex-valued functions over a given path. It is an extension of regular integration, which deals with real-valued functions.

What is the purpose of evaluating complex integration I_c |z^2|?

Evaluating complex integration I_c |z^2| helps us to determine the value of the integral of the complex function |z^2| over a given path. This can be useful in solving problems in various fields such as physics, engineering, and mathematics.

How is complex integration I_c |z^2| different from regular integration?

Complex integration I_c |z^2| involves integrating a complex-valued function over a path in the complex plane, whereas regular integration only deals with real-valued functions over a single variable. Complex integration also takes into account the orientation of the path, which is not considered in regular integration.

What are some common techniques used to evaluate complex integration I_c |z^2|?

Some common techniques used to evaluate complex integration I_c |z^2| include using the Cauchy integral formula, the residue theorem, and contour integration. These techniques involve using various properties of complex functions and complex numbers to simplify the integration process.

Why is evaluating complex integration I_c |z^2| important in science?

Evaluating complex integration I_c |z^2| is important in science because many physical and mathematical problems involve complex functions and require calculating complex integrals. This technique allows scientists to solve complex problems and make accurate predictions in various fields of study.

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