Name_______________________________________
Review #1 for test on Factoring, Radicals, and Imaginary/Complex Numbers
Do all work in your notebook or on separate paper.
Date______
10H Per___
1. Simplify each radical:
a)
112 x 5 y 6 z 7
b)
3
c) 3a  108a13
128a 5 b 3 c 2
2. Perform the indicated operation and express in simplest radical form
a)
4 72  6 54
2 18
c) 8 11b 4  99b 4
b) 2 y 5 y  5 4 y 3
3. Express in simplest a + bi form:
a) (3  i)(2  2i)
b) (3  i)  (2  2i)
4. Rationalize each denominator and express in simplest terms:
a)
5 5
b)
15 2
5 x  15
x3
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5. Simplify: a) i100  i101  i102
c)
b) 3 yi 5 2 yi 56  5i 71
6. What is the additive and multiplicative inverse of
3
4x
9

5  2i
? Express each in simplest a + bi form.
3i
7. If Z1 = -4 + i and Z2 = -2 – 5i
a) Graph(and label) Z1 and Z2.
b) Graph(and label) the sum of Z1 and Z2.
c) Find the absolute value of, Z1, Z2, and (Z1 + Z2) in simplest radical form.
8. Solve each equation for x and check:
a)
2x  5  x  3  1
b) x  1  15  7 x
9. Factor each expression completely (over the set of real numbers):
a) 49  9m 2
b) 4a 2  4a  24
d) 6b 2  b  12
c) x 8a  3x 4a  70
e) 8 x 3  27 y 12
10: Factor completely over the set of complex numbers: 3a 3  2a 2  3a  2
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11. Express the product in simplest form: 2  3b 2 b 4  3b 2  7b
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