Modulus and argument

1. The problem statement, all variables and given/known data
So I'm trying to find the modulus and argument of
cosh(iπ)

2. Relevant equations


3. The attempt at a solution
so far coshπi = ½(e^iπ+e^-iπ) Im now a bit stuck as what to do as i have two terms in the form e^ix and I'm not sure hw to combine them to get the argument?

 

ah is it -1? in that case you'd have ½(-1-1) = -1. so it would just have radius of -1 modulus of π?

 

so modulus of 1 and argument of pi?