1
$\begingroup$

I've been trying to master complex number geometry for some time and now I'm having a hard time finding problems suitable for complex numbers. Can anyone suggest some IMO or other olympiad problem examples, for which complex number geometry would be useful or efficient?

$\endgroup$
3
  • $\begingroup$ IMO problems come from areas included in "math curricula at secondary schools", that's why topics like calculus, complex numbers or solid geometry are excluded in general (though they appeared in few exceptional cases). $\endgroup$
    – user436658
    Jun 2, 2020 at 19:39
  • 1
    $\begingroup$ A good source is the book Complex Numbers from A to...Z by Andreescu and Andrica. Chapter 3 is Complex Numbers in Geometry, Chapter 4 is More on Complex Numbers in Geometry, Chapter 5 is Olympiad-Caliber Problems and Chapter 6 is for Answers, Hints and Solutions. $\endgroup$
    – Sam
    Jun 2, 2020 at 19:45
  • $\begingroup$ If you want something more advanced (way more!), try Geometry of Complex Numbers by Hans Schwerdtfeger. It concentrates on circle geometry, Moebius transformations and non-Euclidean plane geometry, but it kind of exhaust those topics. $\endgroup$
    – Sam
    Jun 2, 2020 at 20:13

1 Answer 1

1
$\begingroup$

My favourite source for learning olympiad-caliber techniques for complex number geometry that also has a great selection of problems amenable to complex number geometry is Euclidean Geometry in Mathematical Olympiads by Evan Chen. The author is a recent IMO gold medalist and he frequently (used to?) post complex number solutions to olympiad geometry problems on a different online math forum, so he has a lot of practical experience in this area of math. The one downside of the book is that it is rife with typographical errors, but this is largely remedied by the list of errata posted on the author's website. I emailed the author to ask if he would publish a corrected version of the book in the near future, and he replied in the negative while expressing regret over not being more careful when he wrote the text.

As already mentioned in the comments, Complex Numbers from A to ... Z, 2nd edition by Andreescu and Andrica is a fantastic resource. However, it is a bit encyclopedic and it can be hard to differentiate without experience between what is is essential knowledge and what should exist in the periphery of your mind.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .