# Idaho - Mathematics: Number and Quantity

## Content Standards | Adopted: 2022

### 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 i^2 = -1, and show that every complex number has the form a + bi where a and b real.

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview

N.CN.A.2: : Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview

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

Points in the Complex Plane

Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview

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 absolute value 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.

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

### N.VM: : Vectors 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

Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview

Vectors

Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview

N.VM.A.2: : Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Adding Vectors

Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview

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

2D Collisions

Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios. 5 Minute Preview

Adding Vectors

Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview

Golf Range

Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable. 5 Minute Preview

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

Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview

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

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

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

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

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

N.VM.C.10: : Demonstrate understanding that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (*x*, *y*) point to be a solution of an equation, or of a system of equations.
5 Minute Preview

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

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

Correlation last revised: 2/28/2022

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