Complex analysis and complex plane

[tsopatsopa]

Homework Statement

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

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

 

[I like Serena]

Welcome to PF, tsopatsopa!

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