Trig & Complex

Algebra Level pending

Let \(z\) be a complex number such that \[z = 2(\cos 3 ^{\circ} + i \cos 87 ^{\circ}). \] Then \( z^{5} \) can be expressed as \( r( \sin \alpha^{\circ} + i \cos \alpha^{\circ}) ,\) where \(r\) is a real number and \( 0 \leq \alpha \leq 90 \). What is the value of \(r + \alpha ?\)

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