# What is the trigonometric form of  7 e^( ( 5 pi)/12 i ) ?

Aug 2, 2018

$7 {e}^{\left(\frac{5 \pi}{12}\right) i} = 7 \cdot \left(\cos \left(\frac{5 \pi}{12}\right) + i \sin \left(\frac{5 \pi}{12}\right)\right)$

#### Explanation:

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

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

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

$7 {e}^{\left(\frac{5 \pi}{12}\right) i} = 7 \cdot \left(\cos \left(\frac{5 \pi}{12}\right) + i \sin \left(\frac{5 \pi}{12}\right)\right)$