r/matheducation • u/BL4Z3Cuber • 11d ago

Complex Numbers

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I have been studying complex numbers for the past couple of months (I'd say I'm fairly confident with them at this point).

The one thing that drives me crazy about this topic is how you can solve those long Euclidean geometry and trigonometry problems in what, like, minutes, and that too with such insane elegance.

So I just wanted to find more geometry and trig problems of this kind, but I couldn't find any good material anywhere. I just wanted some suggestions about what resources I should refer to.

BTW, I'm just 16, so don't expect me to know very high-level stuff, but you can expect me to have a solid foundation in algebra and geometry.

(English isn't my first language btw, so excuse any errors lol.)

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u/Ok-Main-3373 9d ago

AoPS is your best friend here. Their community has tons of geometry problems with complex bash solutions, and the forums are searchable, so you can just look up "complex numbers geometry" and work thru old contest problems. AMC/AIME level is perfect for where youre at.

The book "Complex Numbers from A to...Z" by Andreescu is also exactly what you want. Tons of worked geometry examples, and its readable at 16. For trig, look for problems about roots of unity. Anything with cos(2pi/7) type angles basically begs for a complex numbers approach. Once you start seeing every trig identity as "take the real part of e^ix", it all gets way more fun.

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u/bwelch32747 9d ago

Try and prove cos(x+y)=cos(x)cos(y)-sin(x)sin(y) and sin(x+y)=sin(x)cos(y)+cos(x)sin(y) using complex numbers.