**THE REAL NUMBER SYSTEM (N.RN)**

__EXTEND THE PROPERTIES OF EXPONENTS TO RATIONAL EXPONENTS__**MCC9-12.N.RN.1**Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

*For example, we define 5(1/3) to be the cube root of 5 because we want [5(1/3)] 3 = 5[(1/3) x 3] to hold, so [5(1/3)] 3 must equal 5.*

- During 8th grade, students explore integer exponents, including using scientific notation

**MCC9-12.N.RN.2**Rewrite expressions involving radicals and rational exponents using the properties of exponents.

__USE PROPERTIES OF RATIONAL AND IRRATIONAL NUMBERS__**MCC9-12.N.RN.3**Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

**THE COMPLEX NUMBER SYSTEM (N.CN)**

__PERFORM ARITHMETIC OPERATIONS WITH COMPLEX NUMBERS__**MCC9-12.N.CN.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.

**MCC9-12.N.CN.2**Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

**MCC9-12.N.CN.3 (+)**Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

- Determine quotients of complex numbers only. Use complex numbers in polynomial identities and equations.

**MCC9-12.N.CN.7**Solve quadratic equations with real coefficients that have complex solutions.