# Simple Complex Number Problem

Algebra Level pending

Let $$z_{1} = \sqrt{3} +i5$$ and $$z_{2} = 5 + i\sqrt{3}$$ be two complex numbers. Let $$\alpha_{max}$$ and $$\alpha_{min}$$ be the maximum and minimum values of $$|z_{1} + z_{2}|$$ respectively. What is the value of $$100\lceil \alpha_{max}^{2} - \alpha_{min}^2\rceil$$ ?

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