# Complex Angles

Algebra Level 3

Consider the complex numbers $$w = \sqrt{3} - i$$ and $$z = 2 + 2i$$. The product of these two complex numbers can be written in the form $$r[\cos a^\circ + i\sin a^\circ ]$$, where $$r$$ is a positive real number and $$0^\circ \leq a^\circ < 360^\circ$$. What is the value of $$a$$ (in degrees)?

Details and assumptions

$$i$$ is the imaginary unit, where $$i^2=-1$$.

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