Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Romero Group Title

Explain this identity.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. dpaInc Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm... is that e^(ix) + e^(ix) so = 2e^(ix) on the right side?

    • 2 years ago
  2. Romero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\cos(x)=\frac{e^{ix}+e^{-ix}}{2} \]

    • 2 years ago
  3. Romero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that means I can split cos(x) into two different functions right?

    • 2 years ago
  4. dpaInc Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    what do you mean split up cosx ? that looks a bit like the hperbolic coshx...

    • 2 years ago
  5. Romero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Well there is a problem where I try to show if cos(x) is an eigenfunction of an operator. I did the operation and found out it wasn't but then my book says if it's not a the eigenfunction that it must be a superposition eigenfunction so it splits it into two functions. I just dont see how it splits or how this superposition will be the eigenfunction.

    • 2 years ago
  6. Romero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Can you at least show me how \[\cos(x)=\frac{e^{ix}+e^{-ix}}{2} \]

    • 2 years ago
  7. dpaInc Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    this is guess, but try doing the series expansion for e^(ix) + e^(-ix). i have a feeling the imaginary terms will cancel.

    • 2 years ago
  8. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Write e^ix =cos(x)+i sin(x)

    • 2 years ago
  9. estudier Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    e^(ix) = cos x + i sin x (Euler's Formula) e^(-ix) = cos(-x) + i sin (-x) = cos x- i sin x Add them.

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.