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Taylor series homework problem

  1. Jan 11, 2006 #1
    Dear friends,
    I have a question on a taylor series, that is this one:
    A·e^(i (x))
    That is:
    cos (x)+ i sin (x)
    becouse of the taylor's. But, is this wrong?
    A·e^(v (x)) = cos (x)+ v sin (x) (v is a vector).
  2. jcsd
  3. Jan 11, 2006 #2


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    Are you asking that, since eix=cos x + i sin x, does ev x=cos x + v sin x, where v is a complex number? (I don't know what else you could mean by "vector") If so, no, that is not the case unless v=±i, as you can easily verify using taylor expansions. In fact, just plug in v=1 and you'll see that's obviously not true.
  4. Jan 11, 2006 #3


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    Euler's formula (the one with i in it) is true because of the special properties of i. Generally, your vector will not possess those same special properties of i.
  5. Jan 11, 2006 #4


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    If you try to compute e^(vx) via the Taylor series, what do you get?
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