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13 Results
  • Curriculum Lesson
    Girl Studying

    Precalculus and Advanced Topics Module 1, Topic A, Lesson 4

    Jan 26, 2016 - Student Outcomes Students solve quadratic equations with complex solutions. Students understand the geometric origins of the imaginary unit i in terms of 90-degree rotations.  Students use this...
  • Curriculum Lesson
    Girl's Graduation Day

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 3

    Jan 26, 2016 - 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....
  • Curriculum Lesson
    Lecture Hall

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 2

    Jan 26, 2016 - 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.
  • Curriculum Lesson
    Boy Asking Question to Teacher

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 1

    Jan 26, 2016 - 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...
  • Curriculum Topic
    Students Commencement Ceremony

    Precalculus and Advanced Topics Module 3, Topic A, Overview

    Jan 26, 2016 - 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...
  • Curriculum Lesson
    Students Studying

    Precalculus and Advanced Topics Module 1, Topic C, Lesson 20

    Jan 26, 2016 - 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...
  • Curriculum Lesson
    Girls Studying Together

    Precalculus and Advanced Topics Module 1, Topic C, Lesson 19

    Jan 26, 2016 - 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.
  • Curriculum Lesson
    Student on Computer

    Precalculus and Advanced Topics Module 1, Topic C, Lesson 18

    Jan 26, 2016 - Student Outcomes Students derive the formula for zn = rn(cos(nθ) + i sin(nθ)) and use it to calculate powers of a complex number.
  • Curriculum Topic
    Students Studying

    Precalculus and Advanced Topics Module 1, Topic C, Overview

    Jan 26, 2016 - 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...
  • Curriculum Lesson
    Girls Studying

    Precalculus and Advanced Topics Module 1, Topic B, Lesson 17

    Jan 26, 2016 - 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...
  • Curriculum Lesson
    Group Work

    Precalculus and Advanced Topics Module 1, Topic B, Lesson 16

    Jan 26, 2016 - Student Outcomes Students create a sequence of transformations that produce the geometric effect of reflection across a given line through the origin.
  • Curriculum Module
    Precalculus Module 3 Lesson 7 Diagram

    Precalculus and Advanced Topics Module 3

    Mar 24, 2016 - 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...
  • Curriculum Module
    Student reading

    Precalculus and Advanced Topics Module 1

    Mar 24, 2016 - 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...

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