I have a question on a taylor series, that is this one:
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).
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.
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