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```Name_________________________________
Date_________________
Alg2/Trig
Complex Numbers Review
1. What is the sum of 2  4 and 3  16 expressed in a + bi form?
(1) -1 + 2i
(2) -1 + i 20
(3) -1 + 12i
(4) -14 + i
2. The expression i 0 i 1 i 2 i 3 i 4 is equal to
(1) 1
(2) -1
(3) i
(4) -i
3. If f (x )  x 3  2x 2 , then f i  is equivalent to
(1) -2 + i
4. The expression
(1) 1
(2) -2 – i
i15
is equivalent to
i3
(2) i
(3) 2+ i
(3) -1
(4) 2 – i
(4) -i
5. If a and b are real numbers, then the product of a  bi and a  bi is
(1)
(2)
(3)
(4)
always imaginary
always a real number
sometimes, but not always, a real number
sometimes, but not always, imaginary
6. Which of the following is the additive inverse of -4 + 7i?
(1) -4 – 7i
(2) 4 + 7i
(3)
4 7

i
65 65
(4) 4 – 7i
7. Express the roots of the equation 4x 2  32  0 in simplest a + bi form.
8. Express the multiplicative inverse of 6 – 4i in simplest a + bi form.
a.)
1  i 2 2  i 2 
b.)
1  5i 2  i 
10. Simplify each of the following. Put all answers in simplest a + bi form. Show all
work.
a.
6  8i
3i
b.
2 i
3i
c.
108
2
11. Simplify: (2  i 3)2
13. Simplify:
12. Simplify:
5 
1

  i  7  i 
4 
4

2  5i   3i  5  3  4i 
14. Solve for x and y:
3  x  4yi  10  i
15. Graph and label the complex number u = 2 – 4i and v = -4 – 5i. Then graph and label
u + v.
1. (1)
2. (2)
3. (4)
4. (1)
5. (2)
6. (4)
7. x  2i 2
8.
3
1
 i
26 13
9a. 4  i 2
9b. 7 – 9i
10a.
8
 2i
3
10b.
1 1
 i
2 2
10c. 3i 6
11. 1  4i 3
12.
1 117

i
2 16
13. -6 + 2i
14.
x  7, y 
1
4
```