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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...

 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 solve quadratic equations with complex solutions. Students understand the geometric origins of the imaginary unit i in terms of 90degree rotations. Students use this...

 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.

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Student Outcomes Students determine all solutions of polynomial equations over the set of complex numbers and understand the implications of the fundamental theorem of algebra, especially for...

 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...

 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 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 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 apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.

 Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....