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Help on proofs? pleasee

  1. Sep 6, 2005 #1
    Help on proofs!?! pleasee

    Hi there, I was given these proofs to do for my quantum class.
    proofs are the worst for me, I know it work and i have and idea how it starts which i wrote in the image but I can't seem to figure out the inbetweens. I've attach the images, if anyone can help me that would be great! thanks
     

    Attached Files:

  2. jcsd
  3. Sep 6, 2005 #2
    The first one you do use Taylor expansion and make an observation about regrouping the series with the [tex]\imath[/tex] stuff. The other ones follow from this first proof.
     
  4. Sep 6, 2005 #3
    I'm not so sure how to regroup the i's? do you mean figure out what sin x identity is and cos x idenity and plus it in, in the 2! group and the the other for the 3! group?
     
  5. Sep 6, 2005 #4
    You are on the right track with Part 1.
    The result is known as Euler's formula.
    Look here for more help with the proof
    http://en.wikipedia.org/wiki/Euler's_formula

    You are on the right track with Part 2a.
    You should next use Euler's formula to write
    [tex]
    e^{ia} e^{ib} = (\cos(a) + i \sin(a)) (\cos(b) + i \sin(b))
    [/tex]

    Part 2b) is same approach as part 2a)

    I'm sorry, I don't understand part 3.

    Good luck
     
  6. Sep 6, 2005 #5
    You could prove #2 very easily geometrically.
     
  7. Sep 7, 2005 #6
    Thanks a bunch i understand #1, 2a&b now, can any one help me on the 3rd question?
     
  8. Sep 7, 2005 #7

    Tom Mattson

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    Did you copy #3 exactly as it is written in the book? I am thinking that you did not, because the quesiton as written implies that [itex]z_1*z_2=z_1+z_2[/itex], which is certainly not true.

    Ir's easy enough to find out what you do get when you multiply [itex]z_1[/itex] and [itex]z_2[/itex] together. Just let [itex]z_1=|z_1|e^{i\phi_1}[/itex] and [itex]z_2=|z_2|e^{i\phi_2}[/itex] and multiply them together using the rules for multiplying exponential functions that you learned in precalculus.
     
  9. Sep 7, 2005 #8

    Gokul43201

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