5.4 Complex Numbers

California State Standard N-CN The Complex Number System:
Perform arithmetic operations with complex numbers.
1. Know there is a complex number i such that i 2 = −1, and every complex number has the form a + bi with a and b real. 2. Use the relation i 2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 

Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients]
7. Solve quadratic equations with real coefficients that have complex solutions.
8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i)