# How do you multiply e^((5pi )/ 12 ) * e^( pi i )  in trigonometric form?

$- {e}^{\frac{5 \setminus \pi}{12}}$

#### Explanation:

Using Euler's formula ${e}^{i \setminus \theta} = \setminus \cos \setminus \theta + i \setminus \sin \setminus \theta$ as follows

${e}^{\frac{5 \setminus \pi}{12}} \setminus \cdot {e}^{\setminus \pi i}$

$= {e}^{\frac{5 \setminus \pi}{12}} \left(\setminus \cos \setminus \pi + i \setminus \sin \setminus \pi\right)$

$= {e}^{\frac{5 \setminus \pi}{12}} \left(- 1 + i 0\right)$

$= - {e}^{\frac{5 \setminus \pi}{12}}$