Thread: Complex Analysis: hyperbolic trig and exponential

How would you solve ?

That's not an equation. How can I solve it for anything?

The problem says "Why is the function entire? Write its real part as a function of and , and state why that function must be harmonic elsewhere."

Well, what is the exponential definition of cosh? If you write that out, and then compose it with the exponential, you should be able to apply theorems regarding composition of functions, as well as what you know about the exponential function to achieve the entirety of the function in question. Can you move on from there?