Complex analysis and complex plane

Thread starter tsopatsopa
Start date Jun 25, 2011
Tags

Analysis Complex Complex analysis Complex plane Plane

AI Thread Summary

The discussion focuses on determining the trajectory of the point (u, v) in the complex plane, given the complex function f(z) = u + vi, where u = sin(x) * cosh(y) and v = cos(x) * sinh(y). Participants suggest selecting specific points from the trajectory of z and substituting these values into the function to analyze the resulting trajectory of (u, v). The approach emphasizes practical application by evaluating the function at chosen points. This method aims to visualize how the transformation affects the trajectory in the complex plane. The conversation encourages hands-on exploration of complex analysis concepts.

Jun 25, 2011

tsopatsopa

Homework Statement

Let z= x + yi be a complex number.
and f(z) = u + vi a complex function.
As:
u = sinx\astcoshy
v= cosx\astsinhy

And if z has a trajectory shown in the attached image.
What would be the trajectory of the point (u,v) ?

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Jun 26, 2011

I like Serena

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Welcome to PF, tsopatsopa!

Pick a couple of points on the trajectory and plug the numbers into your function?

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