### N-RN: The Real Number System

#### 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.

Exponents and Power Rules

### N-CN: The Complex Number System

#### 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.

Points in the Complex Plane

#### N-CN.2: Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

#### N-CN.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

#### N-CN.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

Points in the Complex Plane

#### N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.

Roots of a Quadratic

### N-VM: Vector and Matrix Quantities

#### N-VM.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., ??, |??|, ||??||, ??).

Vectors

#### N-VM.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Vectors

#### N-VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions

Golf Range

#### N-VM.4: Add and subtract vectors.

N-VM.4.a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

Adding Vectors

Vectors

N-VM.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Adding Vectors

Vectors

#### N-VM.5: Multiply a vector by a scalar.

Dilations

N-VM.5.a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(???, ?? subscript y) = (c???, c?? subscript y).

Dilations

#### N-VM.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Circles

Ellipses

Hyperbolas

Parabolas

Points, Lines, and Equations

#### N-VM.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Dilations

Translations

Correlation last revised: 9/16/2020