(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the limit points of the set of all points z such that:

a.) [tex]z=1+(-1)^{n}\frac{n}{n+1}[/tex] (n=1, 2, ...)

b.) [tex]z=\frac{1}{m}+\frac{i}{n}[/tex] (m, n=+/-1, +/-2, ...)

c.) [tex]z=\frac{p}{m}+i\frac{q}{n}[/tex] (m, n, p, q=+/1, +/-2 ...)

d.) [tex]|z|<1[/tex]

2. Relevant equations

None.

3. The attempt at a solution

I'm unsure on a.

I'm also unsure on b. I think it's just a bunch of points starting at the line 1 above the real axis and going down. But not totally filled in, so I'd think there'd be no limit points. But then again maybe 0 is a limit point?

c.) I think it's the set of all pts Imz=0

d.) I think it's the set of all pts |z|=1

This is problem 1 on page 29 in Introductory Complex Analysis by Silverman...it's on google books.

http://books.google.com/books?id=Oy...ver&dq=introductory+complex+analysis#PPA29,M1

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# Homework Help: Complex analysis limit points question

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