Question

I need help with this practice problem solvingMake sure to read the instructions on the red line *I have attempted this practice previously and my attempt is in the boxes, though I do not know if I am correct or not, so please disregard it for now (act as if the boxes are empty)

Answer 1

We are asked to determine the following product:

`(3√(3)cis((\pi)/(8)))(3√(5)cis((2\pi)/(3)))`

To solve this product we will first multiply the coefficients:

`(3√(3))(3√(5))(cis((\pi)/(8))cis((2\pi)/(3)))`

Solving the product of the coefficients we get:

`9√(3)√(5)cis((\pi)/(8))cis((2\pi)/(3))`

In order to multiply the square roots we will multiply the numbers inside the radicals:

`9√(15)cis((\pi)/(8))cis((2\pi)/(3))`

Now, we use the following trigonometric identity:

`cis(x)cis(y)=cis(x+y)`

Applying the identity we get:

`9√(15)cis((\pi)/(8)+(2\pi)/(3))`

Adding the values we get:

`9√(15)cis((19\pi)/(24))`

In decimal form, the values are:

`34.86cis(2.49)`