1. 5.7.1 – Complex Numbers

2. We used the method of square roots to solve specific types of quadratics Only used when we had problems such as x 2 – 16 = 0 In all cases, we were taking the square roots of positive numbers

3. Negative Roots But, sometimes we may encounter problems such as; x 2 + 25 = 0 Yields the square root of a negative number Is this possible?

4. Imaginary Number i To help us deal with this problem, we introduce the imaginary unit i Square Roots of Negative Number Properties 1) If r is a positive real number, then √-r = i √r Example; √-7 = i √7 2) i 2 = -1

5. Example. Solve the equation 7x 2 = -49

6. Example. Solve the equation 3x 2 + 5 = -4

7. Example. Solve the equation 4x 2 + 4 = -12

8. Try these 3 problems together. Make sure to note what kind of unit you will need. 1) 5x 2 – 10 = 15 2) -6x 2 = 600 3) 2x 2 + 10 = -10

9. Assignment Pg. 264 3-8 all, 15-25 odd