Crespo UBD Complex Numbers
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This document provides an overview of a unit on complex numbers for an 11th grade Algebra 2 class. The unit objectives are to understand imaginary and complex numbers, and to simplify complex number expressions. Students will learn about the imaginary number i, complex numbers in the form a + bi, and operations like addition, subtraction, and multiplication on complex numbers. They will also learn to use conjugates to find quotients of complex numbers. The unit will be assessed through practice problems, homework assignments, classwork, and an online quiz to evaluate students' understanding of imaginary and complex numbers.
Crespo UBD Complex Numbers
- 1. Grade Level/Subject 11/Algebra 2 Unit Complex Numbers Complex Numbers By Mrs. Crespo SJHS 2013-2014 Stage 1 – Desired Results Objectives: 1. Understand the concept of imaginary numbers. 2. Simplify imaginary numbers. 3. Understand complex numbers. 4. Simplify complex numbers. New York State Standards: The Complex Number System N-CN 1.Know there is a complex number i such that i 2 = −1, and every complex number has the form a + bi with a and b real. 2. Use the relation i 2 = –1 and the commutative, associative, and distributive properties to 3. add, subtract, and multiply complex numbers. 4. (+) Find the conjugate of a complex number; use conjugates to find quotients of complex numbers. Understandings: Students will understand… • Imaginary “i” is −1. • The power of “i” is a 4-phase cycle. • The power of “i” can be evaluated with the cycle and the calculator. • Simplifying imaginary numbers with judicious use of calculator. • Complex numbers have the form a + bi with imaginary and complex parts. • Adding, subtracting, and multiplying complex numbers with thoughtful use of calculator. • Using conjugates to find quotients of complex numbers with proper use of calculator. Essential Questions: • Can we find a number on the number line multiplied by itself two times equals -1? • Instead of the calculator, when do we use the cycle concept to evaluate the value of “i” raised to a given power? • What are the imaginary and the complex parts of a complex number? • How do we apply commutative, associative and distributive properties when simplifying complex numbers? • Do we find the conjugate of the real number or the imaginary number? If so, why? • Do we take the conjugate of the numerator or the denominator to find quotients of complex numbers? • At what instances do we use the calculator to simplify complex numbers? Students will know . . . Students will be able to… • imaginary numbers * evaluate and simplify imaginary numbers • complex numbers * add, subtract, and multiply complex numbers • conjugates of complex numbers * use conjugates to find quotients of complex numbers (division) Stage 2 – Assessment Evidence Performance Tasks: Part 1: Imaginary “i”: Individual Practice (Slide 11 of the PowerPoint on Imaginary “i” and Complex Numbers Part 2: Complex Numbers: Your Turn (Slides 16, 17, 18, 21 of the PowerPoint on Imaginary “i” and Complex Numbers ) Other Evidence: a. Homework: AMSCO Textbook: page 208 3-30 odd only, 35-39 odd only for Part 1 b. Homework: AMSCO Textbook: page 215-216 3-60 every other odd; page 241, 1-40 odd, 53, 55-60 odd, 61-62 for Part 2 c. Classwork: Prentice Hall Review, Page 180-182 1-32 all d. Online Castle Learning Quiz with constructive response entitled “Chapter 5 Quiz 1” Stage 3 – Learning Plan Learning Activities: • Present the lessons through Interactive PowerPoint: Imaginary “i” and Complex Numbers in three 40-minute sessions. • Read the history of complex numbers. • Investigate the application of complex numbers in real life. • Read about fractals at wolfram.com. (Interesting read on how complex numbers create intricate artwork.)