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The points $P,$ $Q,$ and $R$ are represented by the complex numbers $z,$ $(1 + i) z,$ and $2 \overline{z},$ respectively, where $|z| = 1.$ When $P,$ $Q$, and $R$ are not collinear, let $S$ be the fourth vertex of the parallelogram $PQSR.$ What is the maximum distance between $S$ and the origin of the complex plane?

Oct 22, 2019

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in other words, please do not post homework questions on the forum.

Oct 23, 2019
edited by SoulSlayer615  Oct 23, 2019
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