# How do you evaluate  e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i) using trigonometric functions?

In complex terms, $R \left(\sin \theta + i \cos \theta\right)$= $R {e}^{i \theta}$
where $R$ is the modulus and $\theta$ is the argument.
${e}^{\frac{7 \pi}{4} i} - {e}^{\frac{19 \pi}{12} i}$ = $1 \left(\sin \frac{7 \pi}{4} + i \cos \frac{7 \pi}{4}\right)$
- $1 \left(\sin \frac{19 \pi}{12} + i \cos \frac{19 \pi}{12}\right)$
= $\sin \frac{7 \pi}{4} + i \cos \frac{7 \pi}{4}$
- $\sin \frac{19 \pi}{12} + i \cos \frac{19 \pi}{12}$