Question

I need help with this practice problem solving The subject for this is trigonometry, make sure to read the instructions above the red line

Answer 1

The given expressions are

`3√(3)cis(\pi)/(8)=3√(3)(cos(\pi)/(8)+isin(\pi)/(8))`
`3√(5)cis(2\pi)/(3)=3√(5)(cos(2\pi)/(3)+isin(2\pi)/(3))`

To find their product we will multiply the numbers and add the angles

`\begin{gathered} 3√(3)*3√(5)=9√(15) \\ \\ (\pi)/(8)+(2\pi)/(3)=(3\pi)/(24)+(16\pi)/(24)=(19\pi)/(24) \end{gathered}`

Then their product is

`\begin{gathered} 9√(15)(cos(19\pi)/(24)+isin(19\pi)/(24))= \\ 9√(15)(-0.7933533403+i0.608761429) \end{gathered}`

Multiply the number out the bracket by the terms in the bracket

`-27.65+i21.22`

The product of the given terms is

-27.65 + i 21.22

`9√(15)cis((19\pi)/(24))`

The answers are

`\begin{gathered} -27.65+i21.22 \\ 9√(15)cis((19\pi)/(24))=34.86cis((19\pi)/(24)) \end{gathered}`

Write the right side as the answer

`34.86cis((19\pi)/(24))`