Modulus & Arg of cosh(iπ)

The modulus is 1 and the argument is π. In summary, the modulus of cosh(iπ) is 1 and the argument is π.
  • #1
50
0

Homework Statement


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

Homework Equations

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?
 
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  • #2
struggles said:

Homework Statement


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

Homework Equations

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?
 
  • #3
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?
 
  • #4
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.
 
  • #5
so modulus of 1 and argument of pi?
 
  • #6
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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