Countour integral of z from 0 to 1+2i

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Homework Help Overview

The discussion revolves around evaluating a contour integral of the function z from the point 0 to the point 1+2i along the curve defined by y=2x. Participants are exploring the implications of integrating both z and its complex conjugate.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss parametrizing the curve or using the complex antiderivative as potential methods for evaluating the integral. There is also a question about how to approach the integral of the complex conjugate of z, particularly regarding its analyticity.

Discussion Status

The discussion is active, with participants sharing their thoughts on different methods for solving the integral. Some guidance has been offered regarding the approach to the complex conjugate of z, but there is no explicit consensus on the best method to proceed.

Contextual Notes

There is a mention of the complexity of integrating the complex conjugate of z, which is noted to be non-analytical, raising questions about the appropriate methods to use in this context.

doey
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Homework Statement



evaluate contour integral ∫ Z dz from 0 to 1+21 in the curve of y=2x
 
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doey said:

Homework Statement



evaluate contour integral ∫ Z dz from 0 to 1+21 in the curve of y=2x


So what exactly is your problem here? I can think of two ways to do this. Parametrize the curve or use the complex antiderivative. Both are easy. Do something!
 
Last edited:
Dick said:
So what exactly is your problem here? I can think of two ways to do this. Parametrize the curve or use the complex antiderivative. Both are easy. Do something!

ok,i try to solve for integrate z dz= x+iy(dx+idy) and get dy dx from y=2x.and i get the answer for integrate z dz,
how about the answer for integrate complex conjugate of z? since complex conjugate of z is not analytical .can i do it in the same way oso?
 
Last edited:
doey said:
ok,i try to solve for integrate z dz= x+iy(dx+idy) and get dy dx from y=2x.and i get the answer for integrate z dz,
how about the answer for integrate complex conjugate of z? since complex conjugate of z is not analytical .can i do it in the same way oso?

Yes, you can do it in the same way.
 

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