Review and Examples:

1. 7.4 – Adding, Subtracting, Multiplying Radical Expressions Review and Examples:

2. 7.4 – Adding, Subtracting, Multiplying Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

3. 7.4 – Adding, Subtracting, Multiplying Radical Expressions Simplifying Radicals Prior to Adding or Subtracting

4. 7.4 – Adding, Subtracting, Multiplying Radical Expressions

5. 7.4 – Adding, Subtracting, Multiplying Radical Expressions

6. 7.4 – Adding, Subtracting, Multiplying Radical Expressions

7. 7.5 – Rationalizing the Denominator of Radicals Expressions Rationalizing the Denominator Radical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radical is referred to as rationalizing the denominator

8. 7.5 – Rationalizing the Denominator of Radicals Expressions

9. 7.5 – Rationalizing the Denominator of Radicals Expressions

10. 7.5 – Rationalizing the Denominator of Radicals Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required. Review:   (x + 3)(x – 3) x2 – 3x + 3x – 9 x2 – 9   (x + 7)(x – 7) x2 – 7x + 7x – 49 x2 – 49

11. 7.5 – Rationalizing the Denominator of Radicals Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required. conjugate

12. 7.5 – Rationalizing the Denominator of Radicals Expressions conjugate

13. 7.5 – Rationalizing the Denominator of Radicals Expressions conjugate

14. 7.6 – Radical Equations and Problem Solving Radical Equations: The Squaring Property of Equality: Examples:

15. 7.6 – Radical Equations and Problem Solving Suggested Guidelines: 1) Isolate the radical to one side of the equation. 2) Square both sides of the equation. 3) Simplify both sides of the equation. 4) Solve for the variable. 5) Check all solutions in the original equation.

16. 7.6 – Radical Equations and Problem Solving

17. 7.6 – Radical Equations and Problem Solving

18. 7.6 – Radical Equations and Problem Solving no solution

19. 7.6 – Radical Equations and Problem Solving

20. 7.6 – Radical Equations and Problem Solving

21. 7.6 – Radical Equations and Problem Solving

22. 7.6 – Radical Equations and Problem Solving

23. 7.7 – Complex Numbers Complex Number System: This system of numbers consists of the set of real numbers and the set of imaginary numbers. Imaginary Unit: and The imaginary unit is called i, where Square roots of a negative number can be written in terms of i.        

24. 7.7 – Complex Numbers and The imaginary unit is called i, where Operations with Imaginary Numbers             

25. 7.7 – Complex Numbers and The imaginary unit is called i, where Complex Numbers: Numbers that can written in the form a + bi, where a and b are real numbers. 3 + 5i 8 – 9i –13 + i The Sum or Difference of Complex Numbers     

26. 7.7 – Complex Numbers      

27. 7.7 – Complex Numbers Multiplying Complex Numbers        

28. 7.7 – Complex Numbers Multiplying Complex Numbers       

29. 7.7 – Complex Numbers Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    

30. 7.7 – Complex Numbers Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    

31. 7.7 – Complex Numbers Dividing Complex Numbers Complex Conjugates: The complex numbers (a + bi) and (a – bi) are complex conjugates of each other and, (a + bi)(a – bi) = a2 + b2    