N-CN: The Complex Number System

N-CN.A: Perform arithmetic operations with complex numbers.

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

Points in the Complex Plane
Roots of a Quadratic

N-CN.B: Represent complex numbers and their operations on the complex plane.

N-CN.B.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.B.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

N-CN.B.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.

Points in the Complex Plane

N-CN.C: Use complex numbers in polynomial identities and equations.

N-CN.C.7: 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

N-VM.A: Represent and model with vector quantities.

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

Adding Vectors

N-VM.B: Perform operations on vectors.

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

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

Vectors

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

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

Vectors

N-VM.B.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

N-VM.C: Perform operations on matrices and use matrices in applications.

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

Translations

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

Dilations
Translations

Correlation last revised: 1/22/2020

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