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Question

A set of complex numbers is specified. Determine all the boundary points and whether the set is open, closed, open and closed, or not open and not closed. Specify all boundary points of the set (whether or not they belong to the set). V is the set of all z with $2<\operatorname{Re}(z) \leq 3$ and -1 < Imz < 1.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Consider the sketch below.

The set $V$ is the rectangle with vertices at $2+i$, $2-i$, $3+i$ and $3-i$. It is the intersection of the horizontal band (marked red) that contains all numbers whose imaginary part is between $-1$ and 1 and the vertical band (marked blue) that contains all numbers whose real part is between 2 and 3.

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