Question

Find the product of 4cis (pi/4) times 5cis (pi/6) in polar form.

Answer 1

We have the following expression

$4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})$

This is equivalent to

$4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})=(4\times5)cis(\frac{\pi}{4}+\frac{\pi}{6})$

Since

$\frac{\pi}{4}+\frac{\pi}{6}=\frac{6\pi+4\pi}{24}=\frac{10}{24}\pi=\frac{5}{12}\pi$

we have that

$4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})=20cis(\frac{5\pi}{12})$

Therefore, the answer is the second option from top to bottom.