Writing each complex number in exponential form makes this very easy. Recall Euler's formula:
[tex]e^{i\theta}=\cos\theta+i\sin\theta[/tex]
Then
[tex]8(\cos45^\circ+i\sin45^\circ)=8e^{i\pi/4}[/tex]
(since 45º = π/4 rad)
[tex]7(\cos165^\circ+i\sin165^\circ)=7e^{i(11\pi/12)}[/tex]
(since 165º = 11π/12 rad)
The product is
[tex]56e^{i(\pi/4+11\pi/12)}=56e^{i(7\pi/6)}[/tex]
and in Cartesian form this is
[tex]56(\cos210^\circ+i\sin210^\circ)=56\left(-\dfrac{\sqrt3}2-i\dfrac12\right)=\boxed{-28\sqrt3-28i}[/tex]
