Complex Numbers
Definition
A complex number is an expression of the form x + iy, where x, y are real, and i is the imaginary unit.
The real part of a complex number z = x + i y is the real number x (written Re z = x). The imaginary part of z is the real number y (Im z = y).
Equality
Two complex numbers, a + ib and c + i d, are said to be equal if and only if a = c and b = d.
Addition and Subtraction
(a + i b) + (c + i b) = (a + c) + i (b + d)
Multiplication
(a + i b) - (c + i b) = (a - c) + i (b - d)
(a + ib)(c + i d) = (ac - bd) + i (bc + ad)
Division
