# Analytical Functions

1. Jun 14, 2008

### m_s_a

1. The problem statement, all variables and given/known data

Key in writing if possible f (z) with Onley z this mean We can get rid z bar be variable in terms of analytical
Is there a theory or conclude that Ithbt

Or is the only conclusion

2. Jun 14, 2008

### malawi_glenn

What?!?!

3. Jun 15, 2008

### Dick

I'll back malawi_glenn on that. It's really incoherent. But in x+iy, x and y are two independent variables. In the same way, z and zbar are two independent variables. But you are going to have ask a much clearer question before anyone can even figure out what you are talking about.

4. Jun 15, 2008

### m_s_a

I'm sorry the question is
Without the use of Kochi - Riemann's equation
Analytical Function:
Example:
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5. Jun 15, 2008

### m_s_a

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6. Jun 15, 2008

### m_s_a

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7. Jun 15, 2008

### m_s_a

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8. Jun 16, 2008

### Dick

Yes. It's general. d/d(zbar)=0 is the same thing as saying i*d/dx=d/dy using the chain rule for partial derivatives. If you apply that to f=u(x,y)+i*v(x,y) you get the Cauchy-Riemann equations.

9. Jun 16, 2008

### Dick

Basically ok. (n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2). Recheck the sqrt(5i). But remember to be careful how you define 'sqrt' or remember that every nonzero number has two different square roots.

10. Jun 17, 2008

### m_s_a

Thanks

11. Jun 17, 2008

### m_s_a

(n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2).

Excellent