Question

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

Answer 1

We know that the product of two complex numbers follows the property:

`r_1cis(\theta_1)\cdot r_2cis(\theta_2)=r_1\cdot r_2\cdot cis(\theta_1+\theta_2)`

From the problem, we identify:

`\begin{gathered} r_1=3√(3) \\ \theta_1=(\pi)/(8) \\ r_2=3√(5) \\ \theta_2=(2\pi)/(3) \end{gathered}`

Then, using the product property:

`\begin{gathered} 3√(3)cis((\pi)/(8))\cdot3√(5)cis((2\pi)/(3))=3√(3)\cdot3√(5)\cdot cis((\pi)/(8)+(2\pi)/(3)) \\ \\ \Rightarrow3√(3)cis((\pi)/(8))\cdot3√(5)cis((2\pi)/(3))=9√(15)cis((19\pi)/(24)) \end{gathered}`

To the nearest hundredth, this is:

`Answer:34.86cis(2.49)`