Download Operations on Complex Numbers Teacher: Labor Date: 8/12

Operations on Complex Numbers
Teacher: Labor
CA Standard(s):
Date: 8/12 - 16
Subject/Course: Pre-Calculus
Grade: 11th/12th
Alg 1 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers,
including closure properties for the four basic arithmetic operations.
Alg 2 6.0 Students add, subtract, multiply, and divide complex numbers.
Alg 2 25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
Learning Objective (s):
Given two or more complex numbers, the learner will simplify the expression into the standard form of a complex number, a + bi by performing the
necessary arithmetic operation – addition, subtraction, multiplication and/or division
Essential Question(s):
What is the standard form of a complex number?
What are the parts of the standard form?
What is an imaginary number?
How do you add or subtract two or more complex number? multiply two or more complex numbers? divide complex numbers?
What are the steps in rationalizing a complex number in the form
a  bi
?
c  di
When is a complex number considered to be in its simplest form?
What is the conjugate of a complex number?
How is the conjugate different from the inverse of a complex number?

Assessment:
Homework quiz on days 1 and 2, quick check on all days.
Do Now: Writing prompts:
Day 1: “A sign chart is a chart used to…”
Day 2: “A complex number is considered to be in its simplest form when … For example, …”
Day 3: “The inverse of a complex number is different from a conjugate of a complex number. For example, given -3 + 5i,…”
WHOLE GROUP
Do Now: Writing Promts
Lesson: Note-taking (I Do, You Do, We Do): Operations on Complex Numbers
Quick Check
DIRECT INTRUCTION STATION
Unit 1: Linear Equations, Inequalities and
Functions.
Notes: Interactive lecture on number sense
using the set of complex numbers. Students
use their composition notebooks to copy notes.
Students then answer guided exercises and
then answer problems on their own.
Activities:
*Note-taking
*Pair-share
*Mini-whiteboards
*Thumbs up, thumbs down
*I Do, You Do, We Do
*Quick checks
Address possible misconceptions:
Writing a wrong conjugate of a complex number
Wrong use of PEMDAS
COLLABORATIVE STATION
Exploration: Students will be assigned to groups
of 3 or 4 depending on the result of quick checks
or verbal assessments. Students will be working
on complex numbers.
Group Roles:
Leader: Moderates the whole group and
ensures that each member is doing his/her role
Time Keeper: Ensures that each member is on
efficiently on track to accomplish the task
Recorder: Records all responses and makes
sure every one in the group shares the same
data
Reporter: Shares what the group learned from
the activity
INDEPENDENT STATION
Homework Quiz #2: On day 1, students will be
given problems from assigned homework from
the previous day to check for comprehension.
Homework Quiz #3: On day 2, students will be
given problems from assigned homework from
the previous day to check for comprehension.
Individual work: Each student is assigned
homework to build on the concepts discussed in
class.
Day 1 HW:
WSA p56 #19 - 27
Day 2 HW:
Finding the conjugate of a complex
number (worksheet given in class)
Day 3 HW:
WSA p56 #28 - 33
*All HW answers need to be in a composition
notebook