1. Warm Up  Divide the complex number 3 – 2i 1 + i  Multiply the complex number (3 -2i)(1+i)

8. Math IV Lesson11 Complex numbers 2.5 Essential Question: Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

9.  The degree of a polynomial with one variable is the largest exponent of that variable.  Root: where the polynomial is equal to zero.  A quadratic factor with no real zeros is said to be prime.

10. The degree of a polynomial with one variable is the largest exponent of that variable.

11. Roots A root is where the polynomial is equal to zero So, a polynomial of degree 3 will have 3 roots (places where the polynomial is equal to zero). A polynomial of degree 4 will have 4 roots. And so on.

12. Example: what are the roots of x 2 - 9? x 2 - 9 has a degree of 2, so there will be 2 roots. Let us solve it. We want it to be equal to zero: x 2 - 9 = 0 First move the -9 to the other side: x 2 = +9 Then take the square root of both sides: x = ±3 So the roots are -3 and +3

13. A polynomial can be rewritten like this: The factors like (x-r 1 ) are called Linear Factors, because they make a line when you plot them.

14. Polynomials can have complex roots

15. Complex roots always come in pairs Example: x 2 -x+1 Had these roots: 0.5 - 0.866iand0.5 + 0.866i You can either have: No complex roots 2complex roots 4 complex roots 6 complex roots …

16. Factoring a polynomial

17. Use the quadratic formula to solve find the zeros of F(x) = x 2 -12x + 26 QUADRATIC FORMULA

18. Homework P144 # 1-4, 11-19 odd