A geometry problem by Mateus Gomes

Geometry Level 3

For \(z = \dfrac1{\sqrt2} (1+i) \), the value of \( \displaystyle \left | \sum_{k=1}^{60} z^k \right| \) is equal to \(\sqrt{A + B\sqrt B } \), where \(A\) and \(B\) are positive integers. Find \(A+B\).

Clarification: \( i = \sqrt{-1} \).

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