Solving Complex Functions: Evaluating at z=z_0

In summary, the conversation is discussing a mathematical formula and its evaluation at a specific point. The participants are questioning why there are still 'z's in the equation when it has been evaluated at z=z_0. They also discuss the conjugate of the formula and the use of bar notation to denote real arguments.
  • #1
Jerbearrrrrr
127
0
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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  • #2
if z = z_0 in eq. 2 then it makes sense.

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

seems correct. not sure what the question is :p
 
  • #3
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:

1. What is a complex function?

A complex function is a mathematical function that takes complex numbers as inputs and outputs complex numbers. It can be written in the form of f(z) = u(x,y) + iv(x,y), where z = x + iy is a complex number and u(x,y) and v(x,y) are real-valued functions of x and y.

2. What does it mean to evaluate a complex function at z=z0?

Evaluating a complex function at z=z0 means substituting the complex number z0 into the function and calculating the resulting complex number.

3. How do you solve a complex function?

Solving a complex function involves finding the values of x and y that satisfy the equation f(z) = u(x,y) + iv(x,y). This can be done by using algebraic manipulation, substitution, or graphical methods.

4. Why is it important to evaluate complex functions at specific values?

Evaluating complex functions at specific values can help us understand the behavior of the function and make predictions about its properties. It can also be useful in solving equations involving complex functions.

5. What are some common methods for evaluating complex functions at z=z0?

Some common methods for evaluating complex functions at z=z0 include direct substitution, using the Cauchy-Riemann equations, and using the residue theorem. Other methods such as power series expansion and contour integration can also be used depending on the complexity of the function.

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