## y2o2 Group Title Good Question 2 years ago 2 years ago

1. y2o2 Group Title

$\huge y = \cos(i \theta) + i \sin(i \theta)$ prove that y ϵ R

2. AnimalAin Group Title

Use 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.

3. y2o2 Group Title

since : $\huge e^{i \theta } = \cos(\theta) + isin(\theta)$ 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 $\huge y \in \mathbb{R}$