pre-calc day 3 Warm-up: Activities: Learning goal: Be able to write, solve and graph linear and quadratic equations from a variety of initial inputs Activities: Warm-up discussion Text book check out: Review station activitiy Notes on complex numbers Warm-up: Yesterday was labor day: Talk with your table group: What do you know about, and what are your thoughts on labor unions? Be prepared to share some of those thoughts with the class? pre-calc day 3

Quadratic Review Stations Start at any station: spread yourselves out. Work for 4 minutes. Move clockwise to the next station. Timer

Chapter 1 - Sections 5 through 8 Main Ideas Solving a Quadratic Equation 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Graphing a Quadratic Function Quadratic Models Complex Numbers Key Terms Imaginary Unit i Complex Number Complex Conjugates Quadratic Equation Completing the Square Discriminant Quadratic Function Quadratic Model

The complex number system Part ii

Identify the numbers below as rational or irrational numbers

Complex numbers Any number of the form a+bi, where a and b are real numbers and i is the imaginary unit is called a complex number. a is the called the real part and b is called the imaginary part. If b≠0, the number is called an imaginary number.

Numbers Complex numbers a + bi Real numbers Imaginary numbers

The Number System Insert at least two examples for each level. Complex numbers Real Numbers Rational Irrational Imaginary Numbers

Imaginary unit The imaginary unit is i which has the following properties: Now try these

Square root of negative numbers:

=3𝑖−2 5𝑖 =3𝑖−10𝑖=−7𝑖 Example

Examples Multiply (2+3i)(4+5i)= =8+10𝑖+12𝑖+15 𝑖 2 =8−15+22𝑖=−7+22𝑖 Add: (2+3i)+(4+5i) =6+8𝑖 Multiply (2+3i)(4+5i)= =8+10𝑖+12𝑖+15 𝑖 2 =8−15+22𝑖=−7+22𝑖

Dividing; express in form of a+bi.