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Determine the interior, the boundary, and the closure of the set {${z \in :Rez^{2}>1}$}. Prove your statements. Draw a picture of the set (make sure to somehow(perhaps by color) indicate the boundary points which do not belong to the set.) Is the interior of the set path-connected? Prove the statement of your answer.

Trying to brush up on complex analysis. Let me know if you have any guidance for this problem because I am not sure where to even start. Thanks guys.

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If $z=a+ib$, your set can be written $$\lbrace(a,b)\in\mathbb R^2:a^2-b^2>1\rbrace$$ Note that $x^2-y^2=1$ is the equation of a hyperbola.

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