# How can you use trigonometric functions to simplify  15 e^( ( pi)/8 i )  into a non-exponential complex number?

Aug 5, 2018

color(maroon)(=> 13.8585 + 5.7403 i

#### Explanation:

Trigonometric form of ${e}^{i x}$, using Euler's Equation, is given by

${e}^{i x} = \cos x + i \sin x$

$z = | z | {e}^{i x} = | z | \cdot \left(\cos \theta + i \sin \theta\right)$

$15 {e}^{\frac{\pi}{8} i} = 15 \cdot \left(\cos \left(\frac{\pi}{8}\right) + i \sin \left(\frac{\pi}{8}\right)\right)$

$\implies 15 \left(0.9239 + i 0.3827\right)$

color(maroon)(=> 13.8585 + 5.7403 i