1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Adding exponentials

  1. Sep 7, 2013 #1
    1. The problem statement, all variables and given/known data

    How does [itex]\frac{e^{2iz}+2+e^{-2iz}}{4}=\frac{2}{4}[/itex]?

    This is part of something more complex, but this should be enough information. I do not see how those exponentials cancel with each other to leave the [itex]\frac{2}{4}[/itex].

    Thanks
     
  2. jcsd
  3. Sep 7, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    All I can say is that [itex](e^{2iz}+ 2+ e^{-2iz})/4[/itex] is NOT equal to "2/4"! For example, if z= 0, the left side is (1+ 2+ 1)/4= 4/4= 1, not 2/4. And since normally you would write "1/2" rather than "2/4", I seems clear to me that you are missing something. What is true is that [itex]e^{2iz}+ 2+ e^{-2iz}= (e^{iz}+ e^{-iz})^2[/itex]. Does that help?
     
    Last edited by a moderator: Sep 10, 2013
  4. Sep 7, 2013 #3
    Thanks. I knew I wasn't that bad at math to not know how to add exponentials.

    It's from an example in my book. Here is the whole thing:

    Prove that [itex]sin^{2}z+cos^{2}z=1[/itex]

    [itex]sin^{2}z=(\frac{e^{iz}-e^{-iz}}{2i})^{2}=\frac{e^{2iz}-2+e^{-2iz}}{-4}[/itex]

    [itex]cos^{2}z=(\frac{e^{iz}+e^{-iz}}{2})^{2}=\frac{e^{2iz}+2+e^{-2iz}}{4}[/itex]

    [itex]sin^{2}z+cos^{2}z=\frac{2}{4}+\frac{2}{4}=1[/itex]
     
  5. Sep 7, 2013 #4
    Are you still in a doubt? Check the expansion of ##\sin^2z## in the first step, there's a minus sign in the denominator.
     
  6. Sep 7, 2013 #5
    I just tried multiplying the top and bottom of the [itex]sin^{2}z[/itex] expansion by -1 and then adding the two together, I get [itex]\frac{4}{4}[/itex], which is correct. The example makes it look like the exponentials are cancelled before the addition of the two. How did they do that?

    Thanks.
     
  7. Sep 7, 2013 #6
    What do you get when you do that?
     
  8. Sep 7, 2013 #7
    I got [itex]\frac{-e^{2iz}+2-e^{-2iz}}{4}[/itex] and then I added that with the cosine expansion and got 1. But the exponentials didn't disappear until I added the sine and cosine, at which point they cancelled. But in the book, they were gone before the addition of sine and cosine. How did they do that?

    Thanks.
     
  9. Sep 7, 2013 #8
    They were never gone before the addition. Try to add them yourself.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Adding exponentials
  1. Adding exponents (Replies: 4)

  2. Adding Vectors (Replies: 3)

  3. Adding Functions (Replies: 1)

  4. Adding cos (Replies: 5)

  5. Exponential decay (Replies: 2)

Loading...