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y2o2
 2 years ago
Best ResponseYou've already chosen the best response.1\[\huge y = \cos(i \theta) + i \sin(i \theta)\] prove that y ϵ R

AnimalAin
 2 years ago
Best ResponseYou've already chosen the best response.1Use the definitions \[\sin(z)=\frac{e ^{iz}e ^{iz}}{2i}~~~\cos(z)=\frac{e ^{iz}+e ^{iz}}{2}\]Substitute i theta for z, and it will be evident that both terms are real numbers.

y2o2
 2 years ago
Best ResponseYou've already chosen the best response.1since : \[\huge e^{i \theta } = \cos(\theta) + isin(\theta)\] therefore: \[\huge \cos(i \theta) + isin(i \theta) = e^{i i \theta} = e^{ \theta} = ({1 \over e})^{\theta} \] and \[\huge e \ and \ \theta \in \mathbb{R} \] so \[\huge y \in \mathbb{R}\]
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