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What are the boundaries of the sets:

(1) $|z+3|<2$

(2) $|{\bf Im}(z)|<1$

(3) $0<|z-1|<2$

(4) $|z-1|+|z+1|=2$

(5) $|z-1|+|z+1|<3$

(6) ${\bf Re}(z)+1\geq|z|$

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    You have been given a definition in terms of topology for this? It's considered bad form to list a number of problem parts with no effort shown to solve any of them. If nothing else you should have tried to delineate which parts are easier than others. – 2017-02-12

2 Answers 2

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(a)$|z+3|=2$

(b)$|{\bf Im}(z)|=1$

(c)$|z-1|=2$ and $z=1$

(d)$|z-1|=2$ and $|z+1|=2$

(e)$|z-1|=3$ and $|z+1|=3$

(f)$Re(z)-|z|$=-1

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    Please do never ask such a question within an answer. The upvotes or downvotes or comments will tell you if it is correct or not. – 2017-02-03
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    what do you think – 2017-02-03
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What are the boundaries of the sets:

(1) $|z+3|=2$

(2) $|{\bf Im}(z)|=1$

(3) $|z-1|=2$ and $z=1$