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(}(\pi)/(4))\cdot5\text{cis(}(\pi)/(6))`

This is equivalent to

`4\cdot\text{cis(}(\pi)/(4))\cdot5\text{cis(}(\pi)/(6))=(4*5)cis((\pi)/(4)+(\pi)/(6))`

Since

`(\pi)/(4)+(\pi)/(6)=(6\pi+4\pi)/(24)=(10)/(24)\pi=(5)/(12)\pi`

we have that

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

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