 
Summary: Polynomials
Putnam practice
Sept. 24, 2003
1 Complex Numbers
Complex numbers can be written in the form x + iy, where x, y are real
numbers and i =
1. Their addition and multiplication are defined by
(x1 + iy1) + (x2 + iy2) = (x1 + x2) + i(y1 + y2)
and
(x1 + iy1)(x2 + iy2) = (x1x2  y1y2) + i(x1y2 + x2y1)
Every complex number other than 0 has a multiplicative inverse
(x + iy)1
=
x
x2 + y2
 i
y
x2 + y2
We denote the set of complex numbers by C. With the operations of addition
