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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