### N - RN: The Real Number System

#### 1.1: Extend the properties of exponents to rational exponents.

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.

### N - CN: The Complex Number System

#### 3.1: Perform arithmetic operations with complex numbers.

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.

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

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

#### 3.2: Represent complex numbers and their operations on 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.

N-CN.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

N-CN.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

#### 3.3: Use complex numbers in polynomial identities and equations.

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

### N - VM: Vector and Matrix Quantities

#### 4.1: Represent and model with vector 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., v, |v|, ||v||, v).

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

#### 4.2: Perform operations on 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.

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

N-VM.4.c: Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

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

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

N-VM.5.b: Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??. Compute the direction of ???? knowing that when |??|?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ?? < 0).

#### 4.3: Perform operations on matrices and use matrices in applications.

N-VM.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

N-VM.8: Add, subtract, and multiply matrices of appropriate dimensions.

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

Correlation last revised: 9/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.