math quiz 4 1

For  #1 through #6, please put the answer in a + bi form.

 

1.   Add  (3 – 2i) + (-4 – 4i)

 

 

 

 

2.   Subtract  (3– 2i) – (-4– 4i)

 

 

 

 

 

 

3.   Multiply 

 

 

 

 

 

 

 

4.    Divide   

 

 

 

 

 

5.    Square  (1 – i)²

 

 

 

 

 

    To do #6, below, I would use the following table:

 

        

REMAINDER	ANSWER
0	1
1	i
2	-1
3	-i

 

 

FOR EXAMPLE:

Let’s simplify i¹⁰.    We divide whatever the exponent is by 4.

So, doing so, we have

 

    4 goes into 10 a total of 2 times, so

 

       2

     8

     2 

 

We get a remainder of 2, so the answer is -1.   So, we can say that i¹⁰ is -1.

 

 

#6  (a)   Simplify  i⁷¹⁵   

 

 

 

 

       (b)   Simplify  (-3i)⁶

 

 

7.  Solve  x² + 25 = 0

 

 

 

8.   Solve   3x³ + x² – 12x – 4 = 0

 

 

 

 

9.   Solve 4x²–10x  = -3 by completing the square.   Then,

      please leave your answer(s) as APPROXIMATE DECIMAL.

      Then, please check your answer(s) under the word, CHECK,

      below.

 

 

 

 

 

 

 

 

　　　　　　CHECK:

 

 

 

 

 

 

 

 

 

 

 

10.               Solve  -5x²  +  2x  +  1  =  0 by using the quadratic formula. 

                    Then, please leave your answer(s) as EXACT.

                   

 

 

 

 

 

 

 

11.              Using any method you wish, solve x² = x.

 

 

 

 

 

 

 

 

 

12.    Solve  m⁶  +  16m³  +  64  =  0

 

 

 

 

 

13.     Consider the parabola given by the function

          f( x ) = 4x²  –  5x +  9 , and use f( x ) to do each of the  following 

          parts.  

 

(a)   Find the vertex of f( x ).

 

 

 

 

 

 

(b)  Determine whether there is a minimum or maximum

of f and then, use that vertex to find the minimum or maximum of f( x ).  

 

 

 

 

 

(c)   Find the interval where f( x ) is increasing.

 

 

14.             Consider the parabola given by the function

y = -2(x – 1)² – 4 .  

 

(a)  Find the vertex.

 

 

 

 

 

 

(b) Determine whether there is a minimum or maximum

and then, use that vertex to find the minimum or maximum.  

 

 

 

 

 

(c)  Find the interval where the function is decreasing.

 

15.    Solve  .

            Please choose the best possible answer for the solution.

A.      -13

B.     -1, 7

C.       7

D.    No solution

 

 

16.   Solve  

 

 

17.    Solve  

 

 

18.   Solve      for m.

 

 

19.   Solve   for g.

 

 

20.   Charcoal Gurney  has 100 yd of fencing with which to completely enclose

        her rectangular space of briskets.

 

(a)            If the width of the space is x yards, express the area of the space as a function of the width.

 

 

 

 

(b)           Use the function in (a) to find the maximum possible area of the space.