Chapter 7.3, Problem 2E

Find each of the following products. Write each result in both trigonometric and standard form.

$\left[4\left(\cos \frac{\pi }{8}+i\sin \frac{\pi }{8}\right)\right]\left[\cos \frac{5\pi }{8}+i\sin \frac{5\pi }{8}\right]$

$\left[3\left(\cos \frac{7\pi }{6}+i\sin \frac{7\pi }{6}\right)\right]\left[\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3}\right]$

$\left[2\left(\cos \frac{5\pi }{6}+i\sin \frac{5\pi }{6}\right)\right]\left\{3\left[\cos \left(-\frac{\pi }{6}\right)+i\sin \left(-\frac{\pi }{6}\right)\right]\right\}$

$\left[6\left(\cos \frac{5\pi }{3}+i\sin \frac{5\pi }{3}\right)\right]\left\{5\left[\cos \left(-\frac{\pi }{3}\right)+i\sin \left(-\frac{\pi }{3}\right)\right]\right\}$