Taylor series homework problem (1 Viewer)

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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.
 

StatusX

Homework Helper
2,564
1
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.
 

Tide

Science Advisor
Homework Helper
3,078
0
plat,

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.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,829
14
If you try to compute e^(vx) via the Taylor series, what do you get?
 

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