The question
For the mapping f(z) = sinh(z), find and sketch the image of Re(z) = c.
My attempt
Well I tried using the definition of sinh(z) in terms of exponentials:
=
I then used De Moivre's theorem:
The real part of this is:
I'm pretty sure I got this completely wrong.
Can someone explain to me how I'm supposed to attempt this? Any assistance would be greatly appreciated.