Complex Numbers worth it? 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.

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.