# 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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