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

#### 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.

Simplifying Radical 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.

Points in the Complex Plane

Roots of a Quadratic

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

Points in the Complex Plane

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

Points in the Complex Plane

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

Points in the Complex Plane

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

Points in the Complex Plane

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.

Points in the Complex Plane

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

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

Points in the Complex Plane

Roots of a Quadratic

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

Polynomials and Linear Factors

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

Polynomials and Linear Factors

### 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.

Adding Vectors

Vectors

#### 4.2: Perform operations on vectors

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

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

Adding Vectors

Vectors

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

Vectors

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

Vectors

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.

Adding Vectors

Vectors

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

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).

Adding Vectors

Vectors

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

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

Translations

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

Dilations

Translations

Correlation last revised: 1/22/2020