You need to plot the imaginary part of this equal to , so
Now you need to plot this.
For the mapping f(z) = sinh(z), find and sketch the image of Im(z) = d.
If I'm not mistaken, this is just a horizontal line in the z-plane through some constant d. With mapping questions involving Z, I usually try and write f(z) in terms of z, then substitute it into the equation.
However this one has me stumped. I tried:
Let f(z) = w
Now I'm unsure of how to write this in terms of z. Is this the correct approach? If so, how do I progress?