# Is Euler's Identity Applicable to Transforming f(x)=constant*e^(-x^2)?

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• zpatenaude37
In summary, the conversation discusses the use of Euler's identity in the equation f(x)=constant*e^(-x^2) and whether it can be rewritten as f(x)=constant*e^(ix)^2 or put in the form cosx+isinx. The speaker is not familiar with Euler's identity and suggests using an equivalent formula involving sinh and cosh instead.
zpatenaude37
I have a homework question and I am wondering if you can use Eulers identity in this case.

If the equation is f(x)=constant*e^(-x^2) can this be rewritten as f(x)=consant*e^(ix)^2
and then, can you use the identity when it is in this form?

Edit: Can it be put in the form cosx+isinx

I am not well acquainted with Eulers Identity so bear with me

Last edited:
zpatenaude37 said:
I have a homework question and I am wondering if you can use Eulers identity in this case.

If the equation is f(x)=constant*e^(-x^2) can this be rewritten as f(x)=consant*e^(ix)^2
and then, can you use the identity when it is in this form?

I am not well acquainted with Eulers Identity so bear with me
What do you propose to do with $${e^{(ix)}}^2$$

sorry edited for clarity

zpatenaude37 said:
sorry edited for clarity
Sadly ##exp((ix)^2) \ne (exp(ix))^2## if that's what you intended.

You can use ##\exp(-x^2) = \exp(i (ix^2))## and use the Euler formula for that expression, but that gives imaginary arguments for the sine and cosine, which does not look helpful.

zpatenaude37 said:
I have a homework question and I am wondering if you can use Eulers identity in this case.

If the equation is f(x)=constant*e^(-x^2) can this be rewritten as f(x)=consant*e^(ix)^2
and then, can you use the identity when it is in this form?

Edit: Can it be put in the form cosx+isinx

I am not well acquainted with Eulers Identity so bear with me
There is an equivalent formula involving sinh and cosh, but I doubt if it would help you.

## 1. Can Euler's Identity be used in real-life applications?

Yes, Euler's Identity has many practical applications in fields such as physics, engineering, and mathematics. It is used to model and solve complex systems and has been proven to be accurate in various scenarios.

## 2. What is Euler's Identity and how is it used?

Euler's Identity is a mathematical equation that states e^(iπ) + 1 = 0. It is used in complex analysis to relate trigonometric functions with exponential functions, and it also has connections to other important mathematical concepts such as complex numbers and the number pi.

## 3. Is Euler's Identity only applicable to advanced mathematics?

No, Euler's Identity can be understood and used by individuals with a basic understanding of algebra and trigonometry. While it is a fundamental concept in advanced mathematics, it can also be applied in simpler problems and equations.

## 4. Why is Euler's Identity considered one of the most beautiful equations?

Euler's Identity is often referred to as beautiful because it combines five of the most important mathematical constants (e, i, π, 1, and 0) in one concise equation. It also has deep connections to many different areas of mathematics, making it a unifying concept.

## 5. Are there any limitations to using Euler's Identity?

While Euler's Identity is a powerful tool, it does have some limitations. It is not applicable to all mathematical problems and may not always produce accurate results. It is important to understand when and how to use Euler's Identity in order to avoid any potential errors or misconceptions.

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