# Modulus & Arg of cosh(iπ)

• struggles
The modulus is 1 and the argument is π. In summary, the modulus of cosh(iπ) is 1 and the argument is π.

## Homework Statement

So I'm trying to find the modulus and argument of
cosh(iπ)

## The Attempt at a Solution

so far coshπi = ½(e+e-iπ) I am now a bit stuck as what to do as i have two terms in the form eix and I'm not sure homework to combine them to get the argument?

struggles said:

## Homework Statement

So I'm trying to find the modulus and argument of
cosh(iπ)

## The Attempt at a Solution

so far coshπi = ½(e+e-iπ) I am now a bit stuck as what to do as i have two terms in the form eix and I'm not sure homework to combine them to get the argument?
What is the value of e?

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?

struggles said:
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?
cosh(iπ) is indeed equal to -1.

But what are the modulus and the argument? Remember that the modulus is always 0 or positive, never negative.

so modulus of 1 and argument of pi?

struggles said:
so modulus of 1 and argument of pi?
Correct.

## What is the modulus of cosh(iπ)?

The modulus of cosh(iπ) is equal to 1.

## What is the argument of cosh(iπ)?

The argument of cosh(iπ) is equal to iπ.

## Is cosh(iπ) a real or complex number?

cosh(iπ) is a complex number with a real part of 1 and an imaginary part of 0.

## How is cosh(iπ) related to the cosine function?

cosh(iπ) is the hyperbolic cosine function evaluated at iπ.

## What is the significance of cosh(iπ) in mathematics?

cosh(iπ) is important in complex analysis and differential geometry, and it also arises in the study of special functions and hyperbolic geometry.

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