2. SOL Warm Up

4. 1) C 2) B 3) (4x + y) (2x – 5y) 4) x = 7 ½ and x = -1/2 Answers

5. Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary. What is an imaginary number?

6. Definition of imaginary numbers:

7. Simplify complex numbers Remember 28

9. Answer: -i

10. Try these problems: -15 i

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

12. Try these on your own

13. ANSWERS:

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

15. Examples to do together:

16. Lets do another example. FOIL Next

17. Answer: Now try these: 21-i

18. Next

19. Answers:

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

21. are said to be conjugates of each other.

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

23. Reduce the fraction

24. Lets do another example Next

25. Try these problems.

28. Simplify. To figure out where we are in the cycle divide the exponent by 4 and look at the remainder.

29. Simplify. Divide the exponent by 4 and look at the remainder.

30. Simplify. Divide the exponent by 4 and look at the remainder.