Crespo Lesson Plan_Complex Numbers Guide
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This document outlines Mrs. Crespo's PowerPoint presentation on imaginary and complex numbers. The presentation introduces students to imaginary numbers i by discussing square roots of negative numbers. It then provides a brief history of imaginary numbers and defines them. The presentation is divided into two parts: the first focuses on imaginary i, its properties and simplifying expressions involving i. The second part defines complex numbers, plots them on a complex plane, and covers operations like addition, subtraction, multiplication and division of complex numbers. Students complete exit slips and practice problems throughout the lesson to check their understanding.
Crespo Lesson Plan_Complex Numbers Guide
- 1. Mrs. Crespo Algebra 2/Trigonometry SJHS 2013-2014 Mrs. Crespo’s PowerPoint Guide on Imaginary “i” and Complex Numbers (SmartBoard Platform) Procedure: I. Anticipatory Set 1. To prepare the students for the actual lesson on imaginary units and complex numbers, the PowerPoint cover slide is presented. • Ask the students what they observe. Answers vary from noticing the complex number symbol, the graph, to the artwork. Then, inform the student that all the objects on the slide have significant meaning in our pursuit of understanding imaginary “i” and complex numbers. • State that in order to understand complex numbers, we need to know what the imaginary “i" is. To grasp the idea of imaginary “i,” talk about finding square roots with the second slide. II. The second slide opens up reminding the students that when finding the square root, we ask the question, “What number multiplied by itself two times equals the radicand?” • Write examples such as: What is 36? What number do we multiply by itself two times equals 36? What is 49? What number do we multiply by itself two times equals 49? What is 196? What number do we multiply by itself two times equals 196? The students should be able to find the square roots very easily. • Then, tap on the slide and ask “How about this? What is the square root of -1? “ When a student mentions 1. Demonstrate by saying that one times one is one and ask if it’s negative one. When a student responds -1. Illustrate by stating that negative one times negative one is one and ask if it’s negative one. The students will then realize that they couldn’t think of any number. • Bring up the number line by asking if they could find any number on the real number line that when multiplied by itself twice result to negative one. II. Learning Activity: After the students come to terms that they couldn’t find numbers on the real number line for square root of -1, the transition to the actual lesson starts. • Present a brief historical overview, definition, description, and uses of the imaginary “i”. Before getting to the details. Show the changeover slide and say, “Wait. Stop. Yay! How do we work on imaginary numbers? This way, then.” Rafael Bombelli was an Italian mathematician who introduced the idea of imaginary numbers while Renee Descartes was a French mathematician who coined the term “imaginary.” As opposed to Descartes’ opinion that imaginary numbers are literally imaginary, imaginary numbers are actually useful in electrical circuitry, quantum mechanics, and even complex three dimensional images to name a few. The artwork on our cover slide is a fractal created with imaginary numbers.
- 2. Mrs. Crespo Algebra 2/Trigonometry SJHS 2013-2014 PART ONE (Imaginary “i”) 1. Demonstrate the Power of “i.” with the 4-phase cycle. 2. Have the students find the value of a random “i” given a power using the cycle. 3. Show the students how to find the value of “i” using the calculator. 4. Have students find the value of a random “i” given a power using the calculator. 5. On slide 5, model simplifying power of “i” expressions. 6. Click to slide 6 to keep the ball rolling to slide7, then to slide 8 where examples are used to demonstrate simplifying imaginary numbers. The right side of the watering can is used for side notes such as “cake layer” prime factorization. 7. Moving on to slide 9. Demonstrate judicious use of the calculator with the given examples. 8. A brief summary is given. Slides 10 and 11 are shown for individual practice. This can serve as an exit slip. PART TWO (Complex Numbers) 9. Present slide 12 to elaborate on the definition of imaginary numbers; where they are in the set of all numbers. 10. Forward to slide 13. Provide the definition of complex number. Allow the students to provide the real numbers for a complex number example. Let the students determine which part is real and which part is complex. 11. On slides 14 and 15, recall the concept on coordinate plane. Then, introduce the idea of a complex plane. Call on students to provide examples of complex numbers to plot on the complex plane. 12. Before showing the next slides, ask students to take out loose-leaf papers for “Your Turn” that will be collected at the end of the period. 13. With slides 16, 17, and 18, alternately model each operation followed by “Your Turn.” 14. Demonstrate dividing imaginary numbers with slide 19 while recalling the concept on common factors. 15. Introduce conjugates with slide 20. 16. Apply the conjugates in finding the quotient of complex numbers on slide 21. Then, have the student work on “Your Turn.” III. Closure: At the end of each part of the unit, students turn in the exit slip from Part One and the “Your Turn” answers from Part Two, respectively. For quick summary, slide 23 displays several cartoons for a fun way of recalling basic concepts learned.