Question

I need help with this practice The instructions are on the red lineIt asks to fill in the boxes in the picture (I have already attempted this and my answer is in the boxes, I just need to know if I am correct)

Answer 1

Answer:

34.86cis2.49

Explanation:

The given expression as a product is:

$(3\sqrt{3}cis(\frac{π}{8}))(3\sqrt{5}cis(\frac{2π}{3})$

This can be re-expressed as:

$\begin{gathered} (3\sqrt{3})(3\sqrt{5})cis(\frac{π}{8})cis(\frac{2\pi}{3}) \\ 9\sqrt{15}cis(\frac{π}{8})cis(\frac{2\pi}{3}) \end{gathered}$

Note that:

cisAcisB = cis(A+B)

Applying this rule to the expression above, we have:

$\begin{gathered} 9\sqrt{15}cis(\frac{π}{8}+\frac{2\pi}{3}) \\ \\ 9\sqrt{15}c\imaginaryI s(\frac{19\pi}{24}) \\ \\ 34.86cis(\frac{19\times3.14}{24}) \\ \\ 34.86cis2.49 \end{gathered}$