(New page: In any polynomial involving i, i.e. <math>c1*i^n+c2*i^{n-1}+...+c</math> we can express the even powers of i as either 1 or -1. Thus, any polynomial in i can be expressed as <math>c1+c2*i...) |
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More importantly for our class, euler's formula: | More importantly for our class, euler's formula: | ||
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<math>e^{i\pi}=\cos(\theta)+i*\sin(\theta)</math> | <math>e^{i\pi}=\cos(\theta)+i*\sin(\theta)</math> | ||
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also | also | ||
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<math>e^{-i\pi}=\cos(\theta)-i*\sin(\theta)</math> | <math>e^{-i\pi}=\cos(\theta)-i*\sin(\theta)</math> | ||
Revision as of 19:56, 4 September 2008
In any polynomial involving i, i.e. $ c1*i^n+c2*i^{n-1}+...+c $ we can express the even powers of i as either 1 or -1. Thus, any polynomial in i can be expressed as $ c1+c2*i $ where c1 and c2 are any real number constants. This also establishes the set {1, i} as a basis for C as a vector space over all real numbers.
More importantly for our class, euler's formula:
$ e^{i\pi}=\cos(\theta)+i*\sin(\theta) $
also
$ e^{-i\pi}=\cos(\theta)-i*\sin(\theta) $
