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).
Tks.
Are you asking that, since e^{ix}=cos x + i sin x, does e^{v 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.
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.
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