# Taylor Development: Combining cos(z) & cosh(z) in Complex Field

• asi123
In summary, the problem is to develop a Taylor series for the function cos(z) * cosh(z), and the person knows the Taylor series for cos and cosh separately but is unsure how to combine them. They also ask if it matters if the complex field is involved. A possible solution is suggested using the equations cos(z) = (e^iz + e^-iz)/2 and cosh(z) = (e^z + e^-z)/2, but the image is not yet approved. The person thanks the others for their help.
asi123

## Homework Statement

Hey guys.
I need to develop Taylor series for this function (cos(z) * cosh(z)).
I know the Taylor development for cos and the Taylor development for cosh but I have no idea how to combine the two, if it's possible, any idea guys?
And another thing, does it matters if we are talking about the complex field?

Thanks a lot.

## The Attempt at a Solution

#### Attachments

• 1.jpg
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asi123 said:

## Homework Statement

Hey guys.
I need to develop Taylor series for this function (cos(z) * cosh(z)).
I know the Taylor development for cos and the Taylor development for cosh but I have no idea how to combine the two, if it's possible, any idea guys?
And another thing, does it matters if we are talking about the complex field?

Thanks a lot.

## The Attempt at a Solution

cosq= (eiq+ e-iq)/2.
coshq= (eq+ e-q)/2.

might help but you image is yet to be approved.

rootX said:
cosq= (eiq+ e-iq)/2.
coshq= (eq+ e-q)/2.

might help but you image is yet to be approved.

Oh, I see.
I'll try it.
Thanks a lot.

BTW the image only shows the function "cosz * coshz" and the Taylor series of this two functions.

## 1. What is Taylor Development and why is it important?

Taylor Development is a mathematical method used to approximate functions using a series of terms. It is important because it allows us to represent complex functions in a simpler and more manageable form, making them easier to analyze and understand.

## 2. How do you combine cos(z) and cosh(z) in the Complex Field using Taylor Development?

To combine cos(z) and cosh(z) in the Complex Field, we use the Taylor series expansions of both functions and then add them together. This gives us a new series that combines the properties of both cos(z) and cosh(z) in the Complex Field.

## 3. What are the applications of combining cos(z) and cosh(z) in the Complex Field?

Combining cos(z) and cosh(z) in the Complex Field has many applications in various fields of science and engineering. It is used in solving differential equations, signal processing, and in the study of oscillatory and exponential functions.

## 4. How does combining cos(z) and cosh(z) in the Complex Field help in simplifying complex functions?

By combining cos(z) and cosh(z) in the Complex Field, we can represent complex functions in a simpler form, making them easier to analyze and manipulate. This can help in solving complicated problems and understanding the behavior of complex systems.

## 5. Are there any limitations to combining cos(z) and cosh(z) in the Complex Field using Taylor Development?

There are limitations to using Taylor Development to combine cos(z) and cosh(z) in the Complex Field. The method may not work for all functions, and the accuracy of the approximation may decrease as the number of terms in the series increases. Additionally, the convergence of the series may be affected by singularities or branch cuts in the function.

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