### HS.N-RN: The Real Number System

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

HS.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.

#### 1.2: Use properties of rational and irrational numbers

HS.N-RN.4: Perform basic operations on radicals and simplify radicals to write equivalent expressions.

### HS.N-CN: The Complex Number System

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

HS.N-CN.1.i: Know there is an imaginary number i, such that i² = -1, and every complex number has the form a + bi where a and b are real.

HS.N-CN.1.ii: Understand the hierarchical relationships among subsets of the complex number system.

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

HS.N-CN.3: Use conjugates to find quotients of complex numbers.

HS.N-CN.4.i: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers).

HS.N-CN.4.ii: Find moduli (absolute value) of a complex number.

HS.N-CN.4.iii: Explain why the rectangular and polar forms of a given complex number represent the same number.

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

#### 3.2: Use complex numbers in polynomial identities and equations

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

HS.N-CN.9.i: Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions.

HS.N-CN.9.ii: Find all solutions to a polynomial equation.

### HS.N-VM: Vector and Matrix Quantities

#### 4.1: Represent and model with vector quantities

HS.N-VM.1.i: Recognize vector quantities as having both magnitude and direction.

HS.N-VM.1.ii: Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., ??, |??|, ||??||, ??).

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

#### 4.2: Perform operations on vectors

HS.N-VM.4.a.i: Add vectors end-to-end, component-wise, and by the parallelogram rule.

HS.N-VM.4.a.ii: Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

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

HS.N-VM.4.c.i: Understand that vector subtraction v - w is defined as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction.

HS.N-VM.4.c.ii: Represent vector subtraction graphically by connecting the tips in the appropriate order and use the components to perform vector subtraction.

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

HS.N-VM.5.a.i: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction.

HS.N-VM.5.a.ii: Use the components to perform scalar multiplication (e.g., as ??(???, ?? subscript ??) = (?????, ???? subscript ??)).

HS.N-VM.5.b.i: Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??.

HS.N-VM.5.b.ii: Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

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

HS.N-VM.7: Multiply matrices by scalars to produce new matrices.

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

HS.N-VM.12.i: Understand a 2 × 2 matrix as a transformation of the plane.

HS.N-VM.12.ii: 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.