# 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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