To find:
The product of the given complex numbers.
Solution:
It is known that:
[tex]acis(\theta_1)\times bcis(\theta_2)=a\times b\text{ }cis(\theta_1+\theta_2)[/tex]
So, the product of the given complex numbers is:
[tex]\begin{gathered} 3\sqrt{3}cis(\frac{\pi}{8})\times3\sqrt{5}cis(\frac{2\pi}{3})=(3\sqrt{3})(3\sqrt{5})cis(\frac{\pi}{8}+\frac{2\pi}{3}) \\ =9\sqrt{15}cis(\frac{3\pi+16\pi}{24}) \\ =9\sqrt{15}cis(\frac{19\pi}{24}) \end{gathered}[/tex]
Thus, the answer is:
[tex]34.86cis(2.49)[/tex]
