### OH.Math.HSN.RN: The Real Number System

#### OH.Math.HSN.RN.A: Extend the properties of exponents to rational exponents.

OH.Math.HSN.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.

### OH.Math.HSN.CN: The Complex Number System

#### OH.Math.HSN.CN.A: Perform arithmetic operations with complex numbers.

OH.Math.HSN.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.

OH.Math.HSN.CN.2: Use the relation ??²= ?1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

OH.Math.HSN.CN.3: Find the conjugate of a complex number; use conjugates to find magnitudes and quotients of complex numbers.

#### OH.Math.HSN.CN.B: Represent complex numbers and their operations on the complex plane.

OH.Math.HSN.CN.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.

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

OH.Math.HSN.CN.6: Calculate the distance between numbers in the complex plane as the magnitude of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

#### OH.Math.HSN.CN.C: Use complex numbers in polynomial identities and equations.

OH.Math.HSN.CN.7: Solve quadratic equations with real coefficients that have complex solutions.

### OH.Math.HSN.VM: Vector and Matrix Quantities

#### OH.Math.HSN.VM.A: Represent and model with vector quantities.

OH.Math.HSN.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.

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

#### OH.Math.HSN.VM.B: Perform operations on vectors.

OH.Math.HSN.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.

OH.Math.HSN.VM.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

OH.Math.HSN.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.

OH.Math.HSN.VM.5: Multiply a vector by a scalar.

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

OH.Math.HSN.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).

#### OH.Math.HSN.VM.C: Perform operations on matrices, and use matrices in applications.

OH.Math.HSN.VM.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

OH.Math.HSN.VM.8: Add, subtract, and multiply matrices of appropriate dimensions.

OH.Math.HSN.VM.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Correlation last revised: 9/15/2020

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