How can you use trigonometric functions to simplify  14 e^( ( pi)/8 i )  into a non-exponential complex number?

Oct 27, 2016

The complex number is $14 \left(\cos \left(\frac{\pi}{8}\right) + i \sin \left(\frac{\pi}{8}\right)\right)$

Explanation:

Let $z$ be the complex number

So $z = 14 {e}^{i \frac{\pi}{8}}$

We use $z = r {e}^{i \theta} = r \left(\cos \theta + i \sin \theta\right)$

So $r = 14$ and $\theta = \frac{\pi}{8}$

$z = 14 \left(\cos \left(\frac{\pi}{8}\right) + i \sin \left(\frac{\pi}{8}\right)\right)$