Warm Up Solve using square roots Solve by graphing Solve by factoring

HW Check – 5.5

Complex Numbers Section 5.6

Try this: Solve the following quadratic equations by finding the square root: 4x2 + 100 = 0 What happens?

Remember when you first learned to count Remember when you first learned to count? Now, your number system has expanded. You use rational numbers, like ½, and irrational numbers, like . Today, your number system is going to expand to include numbers such as .

i Introducing… This is i. i is defined as the number whose square is -1. and An imaginary number is a number in the form a + bi, where b≠0. Hey. You’re saying I’m not real?!

Imaginary Number: i The Imaginary number This can be used to find the root of any negative number. EX

In your graphing calculator, type and hit enter In your graphing calculator, type and hit enter. What does your calculator say? Choose MODE, and then go down to REAL. Move your cursor to the right once, to a + bi, and press ENTER. This mode allows your calculator to work with Type and hit enter. imaginary numbers! You found me!

Operations with Complex Numbers The Imaginary unit, i, can be treated as a variable Adding & Subtracting Complex Numbers EX: (8 + 3i) + ( -6 + 2i)

Try Some! 7 – (3 + 2i) (4 – 6i) + 3i

Multiplying Complex Numbers Example: (5i)(-4i) Example: (2 + 3i)(-3 + 5i)

Try Some! (6 – 5i)(4 – 3i) (4 – 9i)(4 + 3i)

Now we can SOLVE THIS! Solve 4x2 + 100 = 0

Class Work – Complex Numbers Puzzle Please turn in when complete. This will be your first grade for 4th Quarter!

Homework – 5.6 #s 29 – 40 (skip 31), 72, 77, 78 Last day for make up work is tomorrow by 4:45p! Tutoring after school in 2622.