# Analytical Functions

## Homework Statement

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

malawi_glenn
Homework Helper
What?!?!

Dick
Homework Helper
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.

I'm sorry the question is
Without the use of Kochi - Riemann's equation
Analytical Function:
Example:
[url=http://www.l22l.com][PLAIN]http://www.l22l.com/l22l-up-3/9cfee20d72.bmp[/url][/PLAIN]

Dick
Homework Helper

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.

Dick
Homework Helper

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.

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.

Thanks

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.

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

Excellent