$\displaystyle y''''+y=0$

The characteristic equation yields $\displaystyle r^4=1$

The four roots of unity are 1,-1, i, and -i

I get that $\displaystyle y_{1}=e^x$ and $\displaystyle y_{2}=e^{-x}$, but my book says that $\displaystyle y_{3}=e^{ix}$ reduces to $\displaystyle y_{3}=\cos{x}$ because of Euler's equation. I can't figure out where the $\displaystyle +i\sin{x}$ goes. The same with $\displaystyle y_{4}=\sin{x}$

Any help?