The given expressions are
[tex]3\sqrt{3}cis\frac{\pi}{8}=3\sqrt{3}(cos\frac{\pi}{8}+isin\frac{\pi}{8})[/tex][tex]3\sqrt{5}cis\frac{2\pi}{3}=3\sqrt{5}(cos\frac{2\pi}{3}+isin\frac{2\pi}{3})[/tex]To find their product we will multiply the numbers and add the angles
[tex]\begin{gathered} 3\sqrt{3}\times3\sqrt{5}=9\sqrt{15} \\ \\ \frac{\pi}{8}+\frac{2\pi}{3}=\frac{3\pi}{24}+\frac{16\pi}{24}=\frac{19\pi}{24} \end{gathered}[/tex]Then their product is
[tex]\begin{gathered} 9\sqrt{15}(cos\frac{19\pi}{24}+isin\frac{19\pi}{24})= \\ 9\sqrt{15}(-0.7933533403+i0.608761429) \end{gathered}[/tex]Multiply the number out the bracket by the terms in the bracket
[tex]-27.65+i21.22[/tex]The product of the given terms is
-27.65 + i 21.22
[tex]9\sqrt{15}cis(\frac{19\pi}{24})[/tex]The answers are
[tex]\begin{gathered} -27.65+i21.22 \\ 9\sqrt{15}cis(\frac{19\pi}{24})=34.86cis(\frac{19\pi}{24}) \end{gathered}[/tex]Write the right side as the answer
[tex]34.86cis(\frac{19\pi}{24})[/tex]