Algebra 2 warm up 11.12.13

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  • 1. Algebra 2 Warm up 11.12.13 Solve Each Equation x 2 9 0 x 3 125 0 2 x 2 50 0
  • 2. And now it’s time for.. The Lame Joke of the day.. What did the turkey say to the computer? Google, Google, Google.
  • 3. Definition We know that 2 because (-2)(-2) =4 4 But how do you find and (2)(2) =4 4 ? It is not possible to multiply to numbers together that are the same and get a negative number. Therefore we need what is called imaginary numbers: DEFINITION: i Now we can simplify 1 AND 4 i2 4 1 1 4 i 2i
  • 4. Compare Real 9 25 11 50 Imaginary 3 9 3i 5 25 5i 11 11 i 11 25 2 5 2 50 25 2 5i 2 Summary: You take the square root as normal, but place an “i” to get rid of the negative.
  • 5. To simplify imaginary numbers 1. Imaginary numbers are like terms: Ex: 5i + 3i = 8 i 2. Remember: i 2 1 3. Remove all negatives under square roots before you do anything. 4. You can’t divide by an imaginary number.
  • 6. Examples 16 4i 7i 3i 49 i 2 3i 2 4i 2 4 25 2i 5i 10i 2 10
  • 7. More Examples Most complicated: i 2 i 3 i2 6 6 2 i 2 i i i 2i 2 i 6 2 2i 6 i 2 6 i 2 i 2 i 2 6i 2 6i 2 2i 2 2 3i 2
  • 8. Practice these on your own • The solutions are on the next slide. 3 64 4 3i 9 3i 2 7 2i 2i 6i i 7 4 2 8 4 18 9
  • 9. Check your answers • ANSWERS: 64 9 3i 3i 2 4 4 3i 7 7 7 2 2i 12 2 6i 4 i 3 3 2i 6i i 7 3 8i 8 4 18 5i 2 9 6