Math Is Fun Forum

Well I have a question that is "identify the two interesting points in the picture for the function f(z) = z + 1/z. Explain your answer." where it refers to the tool here:

http://rotormind.com/projects/codework/conformal/

I was told that the 2 interesting points that we must find/prove are:

additionally, there was a hint that the quadratic formula may be useful.

I was also told that I did not need to know anything about conformal mapping and that high school mathematics would enable me to do this question. So my question is  how can I find these points algebraically(they look like -2 and 2)?

note that the solution should not be overly complex as the knowledge required for this is high school maths (including basic complex numbers) and no knowledge of conformal mapping should be shown/used

Thanks!