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 : $i = \sqrt{-1}$ .

The answer is 6.

1 solution

Andreas Wendler
Feb 12, 2016

XPLORE delivers with "abs(sum((1/sqrt(2)*(1+î))^k,k=1 to 60))" value 2.61313 which is squared 6.82843. Now determine the difference with 4 and again the square. We get value 8 equals B^3. Solution is 4+2=6.

A geometry problem by Mateus Gomes

The answer is 6.

1 solution

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