I am supposed to prove that f(z) = e^(-x)e^(-iy) is analytic everywhere. I will be able to do it, I think, but I do not know how to break f(z) into the real and imaginary parts (u(x.y) + iv(x,y)). Can someone please help???

Printable View

- May 15th 2007, 03:31 PMHollystianalytic complex functions
I am supposed to prove that f(z) = e^(-x)e^(-iy) is analytic everywhere. I will be able to do it, I think, but I do not know how to break f(z) into the real and imaginary parts (u(x.y) + iv(x,y)). Can someone please help???

- May 15th 2007, 03:41 PMThePerfectHacker
Hier.

- May 15th 2007, 05:43 PMHollysti
ok, now I am supposed to find the derivative of the function. Do I just add the two partial derivatives?

- May 15th 2007, 07:42 PMThePerfectHacker
It is equal to: u_x + i*v_x

- May 15th 2007, 07:47 PMHollysti
The derivative of e^(-x)e^(-iy) equals u_x + i*v_x? Ok, I hadn't realized that.

- May 15th 2007, 08:15 PMThePerfectHacker
- May 15th 2007, 08:45 PMHollysti
Eulers formula?

- May 15th 2007, 08:52 PMThePerfectHacker
- May 15th 2007, 08:55 PMHollysti
Oh, right. That makes sense. Thank you for taking time to explain that to me!