LAC 28:CXLII.2903. The Complex Number System

A. Perform arithmetic operations with complex numbers. 1. Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real. 2. Use the relation i2= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. B. Use complex numbers in polynomial identities and equations. Limit to quadratics with real coefficients. 1. Solve quadratic equations with real coefficients that have complex solutions. 2. Extend polynomial identities to the complex numbers. 3. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.