Download COMPLEX NUMBERS / ABSOLUE VALUE TEST STUDY GUI

Algebra 2 STUDY GUIDE AII.3 Complex Numbers, AII.4 Absolute Value
Mrs. Grieser
Name: ____________________________________ Date: _______________ Block: _________
COMPLEX NUMBERS / ABSOLUE VALUE TEST STUDY GUIDE
TIPS:

Read over all notes – re-do example questions.

Re-do questions on worksheets and checkpoints.

Answer EVERY QUESTION on this study guide, and check your answers. Do the
ones you get wrong over until you can get them right.

ALWAYS present answers in simplest form – fractions and radicals are reduced, and
there are no radicals or imaginary numbers in denominators.

View videos (Khan Academy or other places – see Mrs. Grieser’s web site for links, or
use Google) or get extra help for concepts you don’t understand.

Don’t wait until the last minute to get help. The day of the test is too late.

When taking the test, answer the questions you know first, then go back and do the
ones that are more difficult.

Wherever possible, check your answers (for example, if it is an equation you are
solving, plug the solution(s) back in).
Practice Questions:
1) Write as complex numbers in a + bi form:
a)
b)
-2
- 72
c)
9 - 5(18)
d)
4  16 - 4(5)
2
2) Simplify the complex numbers by performing the given operations, writing your answers
in a + bi form. No radicals should appear in answers with a denominator, and all
radicals in answers should be in simplest form.
a) (2 – 5i) + (-7 + 2i)
b)
d) (-4 - 6i) – (-3 + 8i)
e) (6 – 2i) + (3 + 5i) - (-4 + 7i)
f) 25 -
h) 5  4 ∙3  9
i) -8  7 ∙5  9
k) (4 + 2i)(2 – 6i)
l) (6 – 8i)(-4 – 10i)
n) (3+6i)(-2+4i) - (1-3i)(5+2i)
o)
g)
 121 -
j) (1 +
 81
 4 )(3 +  49 )
m) (7 + 7i)(7 – 7i)
p)
4  7i
2 - 4i
q)
64 + - 50 - 3.1 +
12
5  2i
-162
c) 7i 3 -
r)
3
 64
12
2i
- 81
25   16
Algebra 2 STUDY GUIDE AII.3 Complex Numbers, AII.4 Absolute Value
Mrs. Grieser Page 2
3) Find the product of 8 + 7i and its conjugate.
4) Find the reciprocal of 10 + 3i in simplest form (no imaginary numbers in denominator).
5) Multiply the conjugate of 5 + 6i with the reciprocal of 7 - 2i.
6) Evaluate the powers of i without a calculator.
a) i215
b) i100
c) i15∙i28∙i75
d) (i21)4
e) (2i)4∙(-5i)3
7) Which expressions are equivalent to 1? Choose all that apply.
a) i24
b) i42
c) i66
d) i82
e) i12∙i28
8) Sam and Sarah are playing a game with complex numbers. Sam picked the number
4 – 3i. Sarah has to select the complex number needed to multiply by Sam’s number to
get a result of 26 – 7i. What number should Sarah select?
9) Solve the equations:
c)
x  10
 1
a) 3|x + 4| = 18
b) 10|7x + 3| = 0
e) |3x + 2| = x - 4
f) 10 - 10|-8x + 4| =10 g) 3 x  7  8
9
10) Solve the equation graphically and algebraically:
|x + 5| - 3 = 0
4
d) 6 – 3|-8x - 9|= -15
h) -4|x - 2| - 9 = -37
Algebra 2 STUDY GUIDE AII.3 Complex Numbers, AII.4 Absolute Value
Mrs. Grieser Page 3
11) Solve the inequalities, writing the solutions in set builder notation, and graphing the
solutions on a number line.
a) |x – 3| > 2
b) |2x – 5| ≤ 5
c) |-3x| ≥ 18
d)
e) |4x| + 5 < -4
f) |7 + 8x| > -89
2x  4
15
 1
12) Graph the equations:
a) f(x) = 2|x|+1
b) f(x) = |3x – 4|
c) f(x) = |x + 2|- 3
d) f(x) = 2|x – 1| + 1
Algebra 2 STUDY GUIDE AII.3 Complex Numbers, AII.4 Absolute Value
Mrs. Grieser Page 4
13) Graph the inequalities:
a) f(x) ≤ |2x – 1|
b) f(x) > |x| - 3
14) A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb.
Write and solve an absolute value inequality that describes acceptable weights for 9.6 lb
bags. Express the solution in set builder notation.
15) The garter snake is a common species in North America. There are various subspecies
and coloration schemes depending on the geographical location. Typical adult garter
snakes range in length from 46 to 130 centimeters. Write an absolute value inequality
that represents the range of lengths of adult garter snakes.
Algebra 2 STUDY GUIDE AII.3 Complex Numbers, AII.4 Absolute Value
Mrs. Grieser Page 5
STUDY GUIDE ANSWERS
1) a) 2i
b) 6i 2
2) a) -5 – 3i
g) 2i
c) 9i d) 2 ± i
b) 4.9 + 14i 2
c) 6i 3
i) 120 7
h) -90
m) 98 n) -41 + 13i o) -6i
d) -1 – 14i e) 13 – 4i f) 25 – 8i
j) -11 + 13i
- 2  3i
p)
2
k) 20 – 20i l) -104 – 28i
60 - 24i
36  45i
q)
r)
29
41
3) 113
4)
5)
6)
7)
8)
10  3i
109
47  32i
53
a) –i
b) 1
a) and e)
5 + 2i
c) -1
d) 1
e) 2000i
1
 3

 c) no solution d)  2,   e) no solution
4
 7

9) a) {-10, 2} b) 
1 
f)  
2
g) {-3, 3}
h) {-5, 9}
10) {-8, -2}
11) a) {x | x > 5 or x < 1};
b) {x| 0 ≤ x ≤ 10};
c) {x | x ≤-6 or x ≥6};
d) { }; 
e) { };  ;
(no solution)
f) {x | x};
(all real numbers)
12) a)
13)
; (no solution)
b)
a) (solid line)
14) {x | 9.24 ≤x ≤ 9.96}
15) |x - 88|≤ 42
c)
d)
b) (dashed line)