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???
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ok, now I am supposed to find the derivative of the function. Do I just add the two partial derivatives?
It is equal to: u_x + i*v_x
The derivative of e^(-x)e^(-iy) equals u_x + i*v_x? Ok, I hadn't realized that.
Originally Posted by Hollysti The derivative of e^(-x)e^(-iy) equals u_x + i*v_x? Ok, I hadn't realized that. But remember to write it in standard form:
In fact, instead we can write,
Originally Posted by Hollysti Eulers formula? No! The Cauchy-Riemann equations.
If f(z) is analytic then u_x = u_y and u_y = -v_x.
Oh, right. That makes sense. Thank you for taking time to explain that to me!
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