Warm Up

1. Warm Up Solve the following equations.

2. 4.4 Complex Numbers (PART 1) The problem is square roots. Every positive number has 2 square roots. So what happens when I want to take the square root of a negative number?

3. Problem with Square Roots Just like every other issue we’ve run into so far, we just introduce a new set of numbers that follow all of the same rules. We call these numbers … IMAGINERY NUMBERS because they cannot physically exist. They can be used to model things such as electricity, so they are still very useful.

4. Imaginary Numbers A pure imaginary number is, . The definition is This means You can multiply by any real number.

5. Square Root Review Simplify the following square roots.

6. Imaginary Numbers Solving a square root of a negative number.

7. Imaginary Numbers Simplify the following square roots.

8. You Try These!!! Simplify the following square roots.

9. Imaginary Numbers The following equations show the first eight powers of .

10. Multiplying Imaginary Numbers Simplify the following.

11. You Try These! Simplify the following.

12. Powers of You can convert a power of to a lower power by taking the closest multiple of 4 that's no bigger than the exponent and subtracting this multiple from the exponent. That is, 99 = 3, because 96 is a multiple of 4, so 96 is just 1, which you can ignore.

13. Powers of In other words, you can… Step 1: divide the exponent by 4, Step 2: discard the answer, and use only the remainder. Step 3: use the remainder to answer the problem.

14. Powers of Simplify the following.

15. You Try These! Simplify the following.

16. Quadratics with Imaginary Solutions So how do imaginary numbers apply to solving quadratics? Solve the following equation. How about this? What’s the difference?

17. Equations with Imaginary Solutions Solve the following equations.

18. You Try These! Solve the following equations.

19. Homework Lesson 4.4 Part 1 Pg. 250 #’s 18-25, 37, 38, 40