N.RN: The Real Number System

1.1: Use properties of rational numbers and irrational numbers.

N.RN.1: Know and apply the properties of integer exponents to generate equivalent numerical and algebraic expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

N.RN.2: 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

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.

Points in the Complex Plane
Roots of a Quadratic

N.CN.2: Use the relation ??² = ?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.

Points in the Complex Plane
Roots of a Quadratic

N.CN.4: Use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

3.2: Represent complex numbers and their operations on the complex plane.

N.CN.5: 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.6: 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

3.3: Use complex numbers in polynomial identities and equations.

N.CN.8: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane
Roots of a Quadratic

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).

Adding Vectors
Vectors

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

Adding Vectors

4.2: Perform operations on vectors.

N.VM.4: Add and subtract vectors.

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

Vectors

N.VM.4c: 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.

Adding Vectors
Vectors

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

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

Dilations
Vectors

N.VM.5b: 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).

Vectors

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

N.VM.8: Add, subtract, and multiply matrices of appropriate dimensions; find determinants of 2×2 matrices.

Solving Linear Systems (Matrices and Special Solutions)
Translations

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