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Warm Up November 18, 2013

Warm Up November 18, 2013. Complete the square 1 . x 2 + 2x – 80 = 0. Imaginary Numbers. Squaring Numbers. What is ? 16 What is - ? 16 *When you multiply 2 negatives, you still get a positive number.

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Warm Up November 18, 2013

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  1. Warm Up November 18, 2013 Complete the square 1. x2 + 2x – 80 = 0

  2. Imaginary Numbers

  3. Squaring Numbers What is ? 16 What is -? 16 *When you multiply 2 negatives, you still get a positive number.

  4. Square Rooting Numbers What is +6 or -6 What is ? hmmmmm… *Here arrives the need for a new number, any ideas?

  5. Introducing Imaginary Numbers Remember radical is an expression that uses a root. The sign is An imaginary number, i, is defined to be and can be used to simplify negative radicals.

  6. Examples 7i 10i 5i

  7. Steps to Simplify Radicals STEP #1: Remove the √(−1)= i. Step #2: Look for “squares”. Take the square root out of the radical. Step #3: Leave anything else under the radical.

  8. 36 64 Remember “Squares” 121 144 25 9 49 4 16 81 100

  9. Examples i i 3i i i 5i i i 4i

  10. Property of i = = -1 = =1

  11. Examples -15

  12. Feeling like you are in an imaginary world??? Be patient Keep trying The more you see it, the easier it gets

  13. Introducing Complex Numbers A complex number is a number with 2 parts: real part and the imaginary part written as: a + bi

  14. Examples -4 + 13i

  15. Examples 10 + i 2 5 + 3i 8 -8 4 + i 4 + 2i

  16. Introducing Conjugates The conjugateof a complex number has the same real part, but an opposite imaginary part.

  17. Examples

  18. Vocabulary Review Real Number Radical Imaginary Number Complex Number Conjugate

  19. Look for a “square” • Real Part? • Imaginary Part? - • Conjugate Remove the “i”

  20. Look for a “square” • Real Part? • Imaginary Part? • Conjugate Remove the “i”

  21. Look for a “square” • Real Part? • Imaginary Part? • Conjugate Remove the “i”

  22. Real Part? • Imaginary Part? • Conjugate Combine like terms

  23. (5 + 2i) (5 + 2i) • Simplify • Real Part? • Imaginary Part? • Conjugate Distribute

  24. 2 2 2 • Look for a “square” • Simplify • Real Part? • Imaginary Part? Remove the “i” • Conjugate

  25. WOW!!! Nice Job working hard today

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