### 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.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.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.B: Perform operations on vectors.

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

N-VM.B.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.

Adding Vectors

Vectors

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

Vectors

N-VM.B.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.

Adding Vectors

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 transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Dilations

Translations

Correlation last revised: 9/24/2019