Use conjugates to find moduli and quotients of complex numbers.
Extend polynomial identities to the complex numbers.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Factor a quadratic to reveal zeros.
Complete the square to reveal maximum or minimum values.
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Understand that rational expressions for a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a non-zero rational expression; add, subtract, multiply, and divide rational expressions.