Math bleg
by rrusczyk, Feb 13, 2009, 6:19 PM
I'm writing a section of the Precalculus book called "Surprises", which consists of surprising applications of complex numbers. That is, it's a collection of problems that don't look like complex number problems, but can be solved quickly and elegantly with complex numbers.
Here are a couple examples:
Evaluate
This proof of Heron by Miles Edwards.
I'd like to have a bunch more. If you have some favorites of your own, please add them. (I'll have a whole section or two dedicated to geometry that's less surprising than the Heron proof.)
Here are a couple examples:
Evaluate
This proof of Heron by Miles Edwards.
I'd like to have a bunch more. If you have some favorites of your own, please add them. (I'll have a whole section or two dedicated to geometry that's less surprising than the Heron proof.)
![\[ \arctan (1/3) + \arctan (1/4) + \arctan (1/5) = \arctan (1/n),\]](http://latex.artofproblemsolving.com/f/e/a/fea544e4ea5402b64c1ebd83e8115f41b4054fe7.png)
and taking the real divided by the imaginary part.![\[ \tan A + \tan B + \tan C = \tan A \tan B \tan C , \]](http://latex.artofproblemsolving.com/3/4/7/3477b4192d0e7e36b67cd4b5335edf59831087ea.png)
,
,
are the angles of a triangle?
February 2012
January 2012