Question: I would like to learn the subject **'complex numbers'**. My goal is to study this on my own. Are there any good tips, books, sites to study this?

Answer: 
I don't know much about knot theory but I know that Meike Akveld taught knot theory at both high school and university level. Here's a bibliography of one of her courses at ETH Zürich:

<https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot/bibliography_FS2015.pdf>

It includes Englisch and German books both for high school and university level. I only list English books for university level:

> 
> General books about knots - accessible to (under-)graduate students:
> 
> 
> * M.A. Armstrong, *Basic Topology*, Undergraduate Texts in Mathematics, Springer-Verlag, 1983 - Chapter 10 is devoted to knots.
> * G. Burde, H. Zieschang, *Knots*, Walter de Gruyter & Co., Berlin, 1985.
> * A.Kawauchi, *A Survey of Knot Theory*, Birkhäuser Verlag, Basel, 1996.
> * W.B.R. Lickorish, An Introduction to Knot Theory, Springer-Verlag. New York, 1997.
> * C. Livingston, *Knotentheorie für Einsteiger*, Vieweg, 1995 (also available in English).
> * K. Murasugi, *Knot Theory & Its Applications*, Chapters 5 and 6, Birkhäuser Boston, 2008.
> * J. Roberts, *Knots Knotes*, unpublished lecture notes, 2010, <http://math.ucsd.edu/~justin/Roberts-Knotes-Jan2015.pdf>.
> * D. Rolfsen, *Knots and Links*, AMS Chelsea Publishing, 2003.
> 
> 
> 

There are still old exercises and solutions from the class available online [here](https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot/uebungen.html). They usually get deleted a year or two after the class, so I'd download them just in case. Plus, you can find some hand-drawn examples on the [lecture website](https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot.html) itself.
You may find the [SageMath knot and links capabilities](http://doc.sagemath.org/html/en/reference/knots/sage/knots/knot.html) useful for computation and visualization.

The [Knot Atlas](http://katlas.org/wiki/Main_Page) might be a bit more comprehensive than you are looking for but is certainly a reference to be quite aware of.