The question:

For the mapping f(z) = sinh(z), find and sketch the image of Re(z) = c

My attempt:

Unless I'm mistaken, Re(z) = C is just a line.

I'm having problems with the f(z) = sinh(z) part. I set f(z) = w, and used the definition of sinh(z) as follows:

Now I'm stuck. :/ Have I attempted this correctly, and if so, how do I proceed? Any help would be greatly appreciated!