Complex Numbers worth it?

Question

Respected readers, I would like to know whether investing a significant amount of time in complex numbers for Olympiad-geometry-bashing and similar stuff (related to Maths Olympiads) is worth the results.

Are the complex numbers useful? Could you tell me some ways they are. If not, what other, better bashing approaches should I invest my time into?

And if you could refer me to a good book to prepare complex numbers from scratch to a nice, advanced level, I would be grateful.

Thanks for your time.

Answer 1

The excellent AoPS text

Rusczyk -- Precalculus

has three chapters on complex numbers.

Those chapters have lots of challenging geometry problems for which complex numbers provide a better insight and a simpler solution.

The entire book is oriented to contest-math-related theory and problems.

Answer 2

OK, so if you are going to an Olympiad, unless you are dealing with world contests or stuff like that, studying on complex numbers is useless.

Most Olympiads are usually focused on testing your problem solving skills, and the ways you solve those problems. They want to see if you can do mathematics fast and accurately.

However, if you are doing an Algebra contest or something like that, I would suggest you do scratch a bit on the surface of complex numbers. Nothing too serious though - that would just be a time-waster.

Finally, there is a very good book on complex numbers, "Complex Numbers from A to Z", by Titu Andreescu, which stretches across everything you need to know about complex numbers.

Hope this helped you! :)