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 Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...

 Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Matrix...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Student Outcomes Students create a sequence of transformations that produce the geometric effect of reflection across a given line through the origin.

 Student Outcomes Students apply their knowledge to understand that multiplication by the reciprocal provides the inverse geometric operation to a rotation and dilation. Students understand the...

 Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...

 Student Outcomes Students derive the formula for zn = rn(cos(nθ) + i sin(nθ)) and use it to calculate powers of a complex number.

 Student Outcomes Students understand how a formula for the nth roots of a complex number is related to powers of a complex number. Students calculate the nth roots of a complex number.

 Student Outcomes Students interpret complex multiplication as the corresponding function of two real variables. Students calculate the amount of rotation and the scale factor of dilation in a...

 Student Outcomes Students represent linear transformations of the form L(x,y) = (ax + by, cx + dy) by matrix multiplication Students recognize when a linear transformation of the form ...

 Student Outcomes Students use matrix transformations to represent motion along a straight line.

 Student Outcomes Students use matrix transformations to model circular motion. Students use coordinate transformations to represent a combination of motions.

 Student Outcomes Students work with 2 × 2 matrices as transformations of the plane. Students understand the role of the multiplicative identity matrix.

 Student Outcomes Students work with 2 × 2 matrices as transformations of the plane. Students combine matrices using matrix multiplication and addition. Students understand the role of the zero matrix...

 Student Outcomes Students understand that the absolute value of the determinant of a 2 × 2 matrix is the area of the image of the unit square.

 Student Outcomes Students understand that 2 × 2 matrix transformations are linear transformations taking straight lines to straight lines. Students understand that the absolute value of the...

 Student Outcomes Students determine inverse matrices using linear systems.

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.

 In Topic A, students look at incidence relationships in networks and encode information about them via highdimensional matrices. Questions on counting routes, the results of combining networks,...

 Student Outcomes Students use matrices to represent and manipulate data from network diagrams.

 Student Outcomes Students use matrices to represent data based on transportation networks. Students multiply a matrix by a scalar, add and subtract matrices of appropriate dimensions, and interpret...

 Student Outcomes Students use matrices to represent data based on transportation networks. Students multiply matrices of appropriate dimensions and interpret the meaning of this arithmetic in terms...

 Topic B explores the geometric context for higherdimensional matrices. The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students...