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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