2. Entry task- Solve two different ways

3. 4.8 Complex Numbers Target: I can identify and perform operations with complex numbers

4. -In the set of real numbers, negative numbers do not have square roots. -Imaginary numbers were invented so that negative numbers would have square roots and certain equations would have solutions. -These numbers were devised using an imaginary unit named i.

5. Imaginary numbers: i is not a variable it is a symbol for a specific number

6. With your a/b partner determine the values for the cycle of i i -i 1 i 1 i -i 1 1

7. Definition of Imaginary Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

8. Definition of Pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

9. Simplify the expression.

10. Remember Simplify each expression. Remember

11. When adding or subtracting complex numbers, combine like terms.

12. Simplify.

14. Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

15. Simplify. F O IL

16. F O I L

17. -Express these numbers in terms of i.

18. Conjugates In order to simplify a fractional complex number, use a conjugate. What is a conjugate?

19. are said to be conjugates of each other.

20. Lets do an example: Rationalize using the conjugate Next

21. Reduce the fraction

22. Lets do another example Next

23. Try these problems.

25. MULTIPLYING COMPLEX NUMBERS

26. ANSWERS (-1)

27. =

28. Use the quadratic formula to solve the following: a=3, b= -2, c=5 4 14

29. Let’s Review 4 You need to be able to: –1) Recognize what i, i 2, i 3 ect. is equal to (slide 5) –2) Simplify Complex numbers –3) Combine like terms (add or subtract) –4) Multiply (FOIL) complex numbers –5) Divide (multiply by complex conjugates)

30. Assignment Pg.253 -254 Homework – #9-43 odds, skip 13,15,17 Challenge - 70