Modulus and Argument of Cosh(iπ)?

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Homework Help Overview

The discussion revolves around finding the modulus and argument of the complex hyperbolic cosine function, specifically cosh(iπ). Participants are exploring the properties of complex numbers and their representations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express cosh(iπ) in terms of exponential functions and are questioning how to combine these terms to determine the argument. There is also a discussion about the value of eiπ and its implications for the modulus and argument.

Discussion Status

Some participants have provided insights regarding the value of cosh(iπ) and its implications for the modulus and argument, while others are still clarifying their understanding of these concepts. There is a mix of interpretations being explored, particularly concerning the nature of modulus in this context.

Contextual Notes

Participants are noting that the modulus should always be non-negative, which raises questions about the interpretation of negative values in their calculations.

struggles
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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(eiπ+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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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(eiπ+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 eiπ?
 
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.
 

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