1. 5.6 Complex Numbers Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. Warm-up (IN) Use the quadratic formula to solve each equation.

2. Notes Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. **Discriminant - then there are 2 real solutions then there is 1 real solution then there are 2 imaginary solutions Determines the # of solutions

3. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 1 – find the discriminant and determine the # of solutions: 1 real solution 2 real solutions

4. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. 2 imaginary solutions Can’t take of a negative #! solve So…we use the imaginary unit, i

5. Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. EX 2 – Solve: Complex number in standard form: real # imaginary #

6. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 3 – Write the expression as a complex number in standard form:

7. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 4 – multiply:

8. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. are called conjugates i cancels out!

9. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. EX 5 – Divide: So…multiply by the conjugate! It cancels out the i! Can’t have i in the denominator!

10. Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers.

11. HW – p. 320 #15-33 (mult of 3), 45-63 (mult of 3), 64,65,68 Out – What can the discriminant tell you about the solutions of a quadratic equation. Summary – I have a question about…or, I get… POW!!