1. Warm Up 1.Evaluate 2. Simplify

3. A Look Ahead Monday: Review for Test Tuesday: Test #1-Complex number system Wednesday-Friday=Polynomials

4. Friendly Reminders All Missing work may be turned in late for half credit (50%) for this unit BY TUESDAY When you are absent, it is your responsibility to check website or with us about what you missed If you are gone on the day before a quiz or test you are still responsible to take the quiz or test Check tutoring schedule I’m always here after school!

5. Quiz Answers and Scores 4 pts each #17 Extra Credit

7. Part I: Evaluate I Divide by 4 & Look at Decimal Reference

8. Part II: Irrational vs. Rational vs. Complex

9. Complex Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals (no fractions) pi, e Imaginary i, 2i, -3-7i, etc.

10. Part III: Simplifying Radicals

13. Part IV: Operations with Radicals

14. Rules Adding and Subtracting 1. Same root 2. Simplify Radicand 3. If radicand=can add/subtract 4. Add/subtract coefficient

17. Rules Multiplying 1. Same root 2. Multiply coefficient 3. Multiply radicand 4. Simplify

18. 1. Distribute “outside” Radical to EVERYTHING inside the parantheses (Remember to talk to everyone at the party) 2. Simplify all radical Expressions Example: Distributing With Radical Expressions

20. Rules Dividing 1. Same root 2. Look to see if you can simplify 3. If not, Multiply numerator and denominator by what’s in denominator

21. You Try!

23. Part V: Operations with Exponents

24. Rules No negative exponents=move to opposite location if negative Anything to the zero power=1

25. Rewriting Power is on top Roots are in the ground

26. Combing with Exponents- + and - To add and subtract with exponents, they must be LIKE TERMS

27. 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 5a 2 + b + 11b 2 – 6 Identify like terms. Add or subtract the coefficients. (3a 2 + 2a 2 ) + (5b – 4b) + 11b 2 – 6 Group like terms.

28. Multiplying Multiplying with exponents =ADD the exponents Example: = = Example: = =

29. Multiplying POWERS “choo-choo train” Separate everything Put like bases together Add exponents of variable bases Multiply numbers!

31. Power to a Power PP: “A power raised to another power” =MULTIPLY the exponents Example: = = Example: = =

32. Power to a Power “Pepe le Pew” Distribute exponent to EVERTHING inside parentheses Simplify number bases Multiply exponents of variable bases

34. Dividing Dividing with exponents =SUBTRACT the exponents Example: = = Example: = =

35. Simplify

37. Part VI: Imaginary

39. Examples of how we use

40. Multiplying Complex Numbers

41. FOIL 1.First 2.Outside 3.Inside 4.Last Method 1: FOIL

42. Dividing Complex Numbers

43. Conjugate -The conjugate of a + bi is a – bi -The conjugate of a – bi is a + bi