Help on proofs? pleasee

  • Thread starter belleamie
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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
 

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  • #2
MalleusScientiarum
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.
 
  • #3
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MalleusScientiarum said:
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.
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?
 
  • #4
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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
 
  • #5
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You could prove #2 very easily geometrically.
 
  • #6
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Thanks a bunch i understand #1, 2a&b now, can any one help me on the 3rd question?
 
  • #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.
 
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