SUBJECT:  PreCal/Trig

GRADE: 11-12

UNIT TITLE: Unit 8 Complex Numbers and Polar Coordinates

TIME FRAME: 4 weeks (3/18 – 4/16)

ESSENTIAL QUESTION:  How are complex numbers, imaginary numbers, and polar coordinates related and applied to real-world situations?

CCSS Standards

Student-Friendly Objectives

Student Learning Experiences/Tasks

Assessment

Vocabulary

Resources: Literary Works/ Websites/ Chapters

N.CN.3  Find the conjugate of a complex number; use conjugates to find moduli

and quotients of complex numbers

Students will be proficient in utilizing the parameters of conjugates, imaginary numbers, and skills associated with conjugates to perform division of complex numbers

Students will work in groups and determine quotients involving complex numbers.

Bellringers, weekly quizzes, chapter tests, peer assessment

Textbook problems (Ch6.6)

Conjugate, complex number, imaginary number, moduli

Textbook (Ch2.5, 6.6)

N.CN.4  Represent complex numbers and their operations 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

Students will be proficient in relating complex numbers to their rectangular and polar forms by graphing them on the complex plane as well as supporting the relationship algebraically.

Students will work in groups of two and graph complex numbers in the complex plane by converting to both rectangular and polar form.

Textbook problems (Ch6.6)

Rectangular form, polar coordinates, complex plane

Textbook (Ch6.4, 6.5, 6.6)

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

Students will be proficient in performing addition, subtraction, and multiplication of complex numbers by utilizing the mechanic of imaginary numbers and conjugates, as well as support theses computations graphically on the complex plane.

Students will perform a project involving a given set of complex numbers, specific operations to perform, and support their conclusions with the use of representations in the complex plane.

Textbook problems (Ch6.5, 6.6)

conjugation

Textbook (Ch6.4-6.6)

N.CN.6  Calculate the distance between numbers in the complex plane as the

Modulus of the difference; calculate the midpoint of

a segment as the average

of the numbers at its endpoints

Students will be proficient in using the Modulus technique for determining the distance between two complex numbers presented in the complex plane, and determine the midpoint of this distance based on the knowledge of the endpoints.

Students will determine the Modulus for the difference of student provided complex numbers and devise a way to determine the distance of half the length of a segment with the respective complex numbers as endpoints.

Textbook Activity per Ch6.6

Modulus, midpoint

Textbook (Ch6,5, 6.6)