Exponential to infinity

  • Thread starter gomes.
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  • #1
58
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Does e^[(-infinity)+(i*w*infinity)] = 0 or 1?

w = omega
 

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Answers and Replies

  • #2
351
1
Well, it's not really quite correct to write that [itex] e^{-\infty+i\omega\infty} [/itex] EQUALS something. But I think you are asking: [tex] \lim_{x\rightarrow\infty} e^{-x+i\omega x} = \lim_{x\rightarrow\infty} e^{-x} e^{i\omega x} [/tex]

Now this last expression has [itex] e^{-x} \rightarrow 0 [/itex] and the imaginary power of [itex] e [/itex] is bounded, so the entire expression goes to 0.
 
  • #3
58
0
thanks! got it now
 

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