Solving Complex Functions: Evaluating at z=z_0

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SUMMARY

The discussion centers on the evaluation of complex functions at a specific point, z=z_0, and the implications of this evaluation on the notation used in the equations. Participants clarify that while substituting z with z_0 in equation (2.11), the presence of 'z's indicates that the function is still being expressed in terms of a variable rather than a constant. Additionally, the conjugate of the function f=u( )+iv( ) is correctly identified as u( )-iv( ). The distinction between f*(z) and f(z*) is confirmed, emphasizing that the evaluation process does not eliminate all instances of 'z' in the equation.

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  • Understanding of complex functions and their evaluations.
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Students and professionals in mathematics, particularly those studying complex analysis, as well as educators looking to clarify concepts related to function evaluation and notation.

Jerbearrrrrr
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Hi, just wondering where this line comes from

[PLAIN]http://img514.imageshack.us/img514/4990/complq.jpg

Here's my beef:

If we evaluate it at z=z_0, why are there still 'z's in (2.11)?
Furthermore, isn't the congujate of f=u( )+iv( ) simply u( )-iv( )?

The formula seems to have been evaluated at z* = z*_0.

Not sure what's going on.
Thanks
[edit]
If this belongs in the homework thing forum place, sorry. Please move it.
 
Last edited by a moderator:
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if z = z_0 in eq. 2 then it makes sense.

f*(z) =/= f(z*)

seems correct. not sure what the question is :p
 
Why are there still z's in the 2nd equation?
as in, shouldn't they all be z_0s now?

[edit]
I think the author has 'barred' the arguments because they are real, after setting z=z_0 and leaving z* as it is.
 
Last edited:

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