1. Complex Numbers Advanced Math Topics Mrs. Mongold

2. Can you find the square root of a number? Lets see…

3. What about the sqare root of a number that isnt a perfect square?

4. So Lets Review… To find the square root of negative numbers you need to use imaginary numbers. i is the imaginary unit i 2 = -1 i =

5. What about the square root of a negative number?

6. The Square Root Property For any real number n, if x 2 =n, then x = ±

7. Lets Practice With i Simplify -2i (7i) (2 – 2i) + (3 + 5i) i 45 i 31

8. Solve 3x 2 + 48 = 0 4x 2 + 100 = 0 x 2 + 4= 0

9. More with Complex Numbers Multiply (3 + 4i) (3 – 4i) (1 – 4i) (2 + i) (1 + 3i) (7 – 5i) (2 + 6i) (5 – 3i)

10. More with Complex numbers Conjugate: a binomial with the opposite sign as the original binomial Given 2-i the conjugate is 2+i You use the conjugate to simplify a fraction containing imaginary numbers

11. Cant have i in the denominator Divide 3i 2 + 4i -2i 3 + 5i 2 + i 1 - i

12. More division 5 + i 2i 4 – i 5i

13. Homework Page 503/3-72 multiples of 3