Euler's Formula (1 Viewer)

[Js^-1]

Hey I have been looking on the forums and I found a lot of references to eⁱ^θ = cis θ

I have been looking, but have been unable to find, a proof for this formula. If anyone can post up a proof, or a link to one, that would be awesome.

 

[Iruka]

Do you know about Taylor series?

 

[Js^-1]

Ah I've heard of it...Something about expressing numbers as a finite series or something? I've never actually learnt it.

 

[Iruka]

Transcendental functions like sine, cos and exp can be expressed as a Taylor series.

http://en.wikipedia.org/wiki/Taylor_series

I believe Euler proved the formula by showing that the Taylor series of both sides of that equation are equal.

 

[lolokay]

http://en.wikipedia.org/wiki/Euler's_formula#Proofs
how hard were you looking? =/

 

[Js^-1]

Only on the BOS forums...Wikipedia tends to have overly complicated articles about mathematics and/or science that aren't all too easy to understand.

 

[me121]

Only on the BOS forums...Wikipedia tends to have overly complicated articles about mathematics and/or science that aren't all too easy to understand.

i disagree.. i tend to find that wikipedia articles are good at explain maths. (for example the word manifold pops up heaps in higher years maths however the wikipedia article explains it really well http://en.wikipedia.org/wiki/Manifold)