- #1

richyw

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## Homework Statement

My textbook gives me this definition of a connected set.

http://media.newschoolers.com/uploads/images/17/00/69/80/76/698076.png

I have been working through my practice problems and I got to one that asked me to sketch the set given by[tex]|z+2-i|=2[/tex]and note whether it is open/closed/neither bounded/unbounded and if it is connected

## Homework Equations

[itex]|z-z_a|=r[/itex] describes a circle with centre [itex]z_a[/itex] and radius r

## The Attempt at a Solution

so I have drawn a circle with centre at (-2,i) and radius 2. It contains all of its boundary, so I said it was closed, it can be contained within a circle centred at the origin, so I said it was bounded.

now about the connectedness. The definition my textbook gives me says I need to be able to connect two points in S, using a finite number of lines that are contained in S. The only way I can connect two points in S is by following a circular path. I don't think that a circular path can be made up of a finite number of lines? but apparently this is a connected set. Can someone please explain to me where I am misinterpreting my textbook?

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