1. Help Simplify the following completely, show all work.

(45)

2. Please help Simplify the following completely, show all work. (49)

3. Help Simplify the following completely, show all work. 4+(27)

4. Help Explain the pattern in the simplification of imaginary numbers (Hint: i¹,i²,i³,i⁴,i⁵,dots.... )

5. Help Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all steps of the process, including the solution and to which number set it belongs.

6. Without graphing, determine the vertex, domain, and range for each of the functions. Does the vertex of each function represent a maximum point or a minimum point? Show all algebraic work to calculate the vertices. f(x)=(x+4)² +3

7. Without graphing, determine the vertex, domain, and range for each of the functions. Does the vertex of each function represent a maximum point or a minimum point? Show all algebraic work to calculate the vertices. g(x)=- x² - 6x + 7

8.Help Calculate the discriminant, explain what type of solution can be expected, and which method of solving would be best for each given this information. f(x)=x²- 4x + 7

9. Calculate the discriminant, explain what type of solution can be expected, and which method of solving would be best for each given this information. g(x)=-x²-3x+13