I'm a little stuck on the following problem:
How many of the roots to the equation:
z - e^z + 5 = 0
lie in the region Re(z) < 0?
I'm just not sure how to approach this. I've solved similar problems through Rouche's theorem, but in all those cases I'm finding the number of roots within a closed circular contour. Here I really don't know what to do! Any help will be greatly appreciated!