1. Directions- Solve the operations for the complex numbers.
Do Now #9
Directions- Solve the operations for the complex numbers.
(3i+2)-(12+2i)
(5i+3)(6i-4)
(9i-3)
(3i-2)

2. Stations
Trig Review
Computing Complex numbers

3. 5.6 – Quadratic Equations and Complex Numbers
Objectives:
Classify and find all roots of a quadratic equation.
Graph and perform operations on complex numbers.
Standard:
C. Present mathematical procedures and results clearly, systematically, succinctly and correctly.

4. x – intercepts *Solutions *Roots *Zeroes
The Solutions to a Quadratic Equation can referred to as ANY of the following:
x – intercepts
*Solutions
*Roots
*Zeroes

5. Discriminant
The expression b2– 4ac is called the discriminant of a quadratic equation.
If b2– 4ac > 0 (positive), the formula will give two real number solutions.
If b2– 4ac = 0, there will be one real number solution, called a double root.
If b2– 4ac < 0 (negative), the formula gives no real solutions

6. Ex 1. Find the discriminant for each equation
Ex 1. Find the discriminant for each equation. Then determine the number of real solutions for each equation by using the discriminant.

7. Imaginary Numbers
If r > 0, then the imaginary number is defined as follows:
Example 1a

8. Example 1b *
-4x2 + 5x – 3 = 0

9. Example 1c *
6x2 – 3x + 1 = 0

10. Complex Numbers

11. Example 1a and b*
b. 2x + 3iy = i

12. Operations with Complex Numbers
c. (-10 – 6i) + (8 – i)

13. Multiply
a. (2 + i)(-5 – 3i)
b. (6 – 4i)(5 – 4i)
c. (2 – i)(-3 – 4i)

14. Conjugate of a Complex Number
The conjugate of a complex number a + bi is a – bi.
To simplify a quotient with an imaginary number in the denominator, multiply by a fraction equal to 1, using the conjugate of the denominator.
This process is called rationalizing the denominator.

15. 4+3i
5 - 4i
-7+ 6i
-9 - i

16. Example 1a
Rationalize the fraction:

17. Example 1b
Rationalize the fraction:

18. Writing Questions

20. Homework
Integrated Algebra II- Section 5.6 Level A
Honors Algebra II- Section 5.6 Level B