Question

I need help with this practice problem solving The subject is trigonometry k-12Make sure to read the instructions above the red line

Answer 1

To find:

The product of the given complex numbers.

Solution:

It is known that:

`acis(\theta_1)* bcis(\theta_2)=a* b\text{ }cis(\theta_1+\theta_2)`

So, the product of the given complex numbers is:

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

Thus, the answer is:

`34.86cis(2.49)`