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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