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

[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

 

[PeroK]

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 $${e^{(ix)}}^2$$

 

[zpatenaude37]

sorry edited for clarity

 

[PeroK]

sorry edited for clarity

Sadly $exp((ix)^2) \ne (exp(ix))^2$ if that's what you intended.

 

[mfb]

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.

 

[mathman]

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.