Imaginary Numbers and Operations Explained
Explore the historical background, mathematical significance, and operations involving imaginary numbers through engaging visuals and activities. Learn how imaginary numbers complement real numbers in complex arithmetic.
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Presentation Transcript
Imaginary Numbers Operations explained? 1
Goals for today: How did we get to imaginary numbers historically? (slide 4) 2. Why is there a need for imaginary numbers mathematically?(slide 5) a. We have gotten along fine without them until now? 3. Where do I put them? (slide 6) a. Why are they complex? 4. What does adding and subtracting complex numbers look like? (slide 7) 5. What does multiplying complex numbers look like? (slide 8) 1. 2
What math words do you recognize? Math Humor - Not Imaginary. 3
A little history - RUUUUMMMMMBBBBLLLLEE 1. You will have five minutes to research your historical figure. 2. Be ready to explain how your figure relates to any one or few of these words. a. Negative or positive numbers (1 point) b. Complex numbers (1 point) c. Imaginary numbers (1 point) d. Complex number plane (1 point) e. Number line (1 point) 3. Be ready to explain how they relate to one of the other historical figures. 2 points for each connection 4
Number line Cha - Cha Objective: Place yourself on the number line given your number and the position of zero ( my hero!) 1. Take a number 2. Find your place on the line. 3. Be ready to answer some rather obvious or oblivious questions (Remember you are the math hero here!) 5
A Real- Imaginary Number Plane Real numbers have inverses. -1 ------ 1 Imaginary numbers rotate. i 1 -1 -i 6
What does adding complex numbers look like? real part + imaginary part ( a + bi) (2 +3i) + (-6 + 4i) 7
What does multiplying look like? real part + imaginary part ( a + bi) (-2 + i) (4 + 5i) 8
So what did we learn?? Math does NOT come in a box it develops Imaginary numbers exist to because they are actual solutions. Imaginary numbers do not exist on the real number line. When we operate on real numbers, actual physical things happen. 9
