Answer :

[tex]cis(\theta)=e^{i\theta}=cos\theta+i\cdot sin\theta[/tex]

Then we have:

[tex]\begin{gathered} [3\sqrt{3}\cdot cis(\frac{\pi}{8})\rbrack\cdot[3\sqrt{5}\cdot cis(\frac{2\pi}{3})\rbrack=(3\sqrt{3}\cdot3\sqrt{5})e^{i\frac{\pi}{8}}\cdot e^{i\frac{2\pi}{3}} \\ [3\sqrt{3}\cdot cis(\frac{\pi}{8})\rbrack\cdot[3\sqrt{5}\cdot cis(\frac{2\pi}{3})\rbrack=9\sqrt{15}e^{i\frac{19\pi}{24}} \\ [3\sqrt{3}\cdot cis(\frac{\pi}{8})\rbrack\cdot[3\sqrt{5}\cdot cis(\frac{2\pi}{3})\rbrack=9\sqrt{15}cis(\frac{19\pi}{24}) \end{gathered}[/tex]

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