How would you solve $\displaystyle \cosh e^z$?

Printable View

- Jun 19th 2010, 01:27 PMseadogComplex Analysis: hyperbolic trig and exponential
How would you solve $\displaystyle \cosh e^z$?

- Jun 19th 2010, 01:36 PMAckbeet
That's not an equation. How can I solve it for anything?

- Jun 19th 2010, 02:45 PMseadog
The problem says "Why is the function $\displaystyle \cosh e^z$ entire? Write its real part as a function of $\displaystyle x$ and $\displaystyle y$, and state why that function must be harmonic elsewhere."

- Jun 19th 2010, 05:15 PMAckbeet
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?