Complex determinants
by v_Enhance, Jan 12, 2013, 8:00 AM
worked on today's WOOT PotD! Kept on seeing "\bar y" while typing the TeX, though.
But seriously, determinants are a lot more useful than they get credit for. They let you hold symmetric information and do several useful row operations. (It takes some time to get used to, though.)
Like, to prove three complex numbers
are collinear, it's a lot more natural to do manipulations with 
than to do something asymmetric with 
. Not only that, you can lop off any common stuff by just subtracting the third column from the other two, and so on.
Good example: USAMO 2012 #5.
But seriously, determinants are a lot more useful than they get credit for. They let you hold symmetric information and do several useful row operations. (It takes some time to get used to, though.)
Like, to prove three complex numbers
are collinear, it's a lot more natural to do manipulations with 
than to do something asymmetric with 
. Not only that, you can lop off any common stuff by just subtracting the third column from the other two, and so on.Good example: USAMO 2012 #5.
This post has been edited 2 times. Last edited by v_Enhance, Jan 12, 2013, 8:03 AM
i just gave up on training 
April 2023
February 2023