Download A2.N.9: Multiplication and Division of Complex Numbers 3: Perform

Regents Exam Questions
A2.N.9: Multiplication and Division of Complex Numbers 3
Name: ________________________
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A2.N.9: Multiplication and Division of Complex Numbers 3: Perform arithmetic operations on
complex numbers and write the answer in the form a+bi
1 Express in
form: 2 (
2 Express 3 1
in
3)
form.
3 Express the product (3 2 )(1 3 ) in
form.
4 Express the product 2
(4 3 ) in the form
5 Show that the product of
+
.
and its conjugate is a real number.
6 In an electrical circuit, the voltage, , in volts, the current, , in amps, and the opposition to the flow of current,
called impedance, , in ohms, are related by the equation
. A circuit has a current of (3 ) amps and an
impedance of ( 2 ) ohms. Determine the voltage in
form.
7 Express 3 2
2
in
form.
is equal to (2
8 The complex number
form: (2
9 Express in simplest
)3
10 Express the complex number (1 2 ) 4 in
11 Expand and express (
) 2 What is the value of ?
3) 4 in simplest
form.
form, where is the imaginary unit.
12 Where is the imaginary unit, expand and simplify completely (3
13 Express
5
2
in simplest
form.
1
)4 .
ID: A
A2.N.9: Multiplication and Division of Complex Numbers 3: Perform arithmetic operations on
complex numbers and write the answer in the form a+bi
Answer Section
1 ANS:
2 6
PTS: 2
2 ANS:
3 3
REF: 018714siii
PTS: 2
3 ANS:
9 7
REF: 089012siii
PTS: 2
4 ANS:
11 2
REF: 088616siii
PTS: 2
5 ANS:
(
)(
REF: 068911siii
)
2
Since
and
are real, their squares are real and the sum of their squares is real.
2 2
2
2
2
( 1)
2
PTS: 2
6 ANS:
7
REF: 080122b
PTS: 2
7 ANS:
5 12
REF: 010325b
PTS: 2
8 ANS:
3
REF: 069014siii
PTS: 2
9 ANS:
2 11
REF: 080621b
PTS: 3
REF: 089339siii
1
ID: A
10 ANS:
7 24
PTS: 6
11 ANS:
28 96
REF: 069440siii
PTS: 5
12 ANS:
28 96
REF: 069940siii
PTS: 4
13 ANS:
2
REF: 080141siii
PTS: 2
REF: 089612siii
2
Regents Exam Questions A2.A.7: Factoring Polynomials 1
Name: ________________________
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A2.A.7: Factoring Polynomials 1: Factor polynomial expressions completely using common
factor extraction, difference of perfect squares, quadratic trinomials
1 Factored completely, the expression 6x x 3
1) x(x 3)(x 2)
2) x(x 3)(x 2)
2 Factored completely, the expression 12x 4
1) x 2 (4x 6)(3x 2)
2)
2(2x 2
3x)(3x 2
3 Factor: 2x 2
3x 2
4 Factor: 4a 2
9a 9
5 Factor: 3a 2
a 2
2x)
6 Factor: 10x 2
11x 6
7 Factor: 4a 2
11a 20
8 Factor: 3x 2
5x 12
9 Factor: 12a 2
x 2 is equivalent to
3)
x(x 3)(x 2)
4)
x(x 3)(x 2)
10x 3 12x 2 is equivalent to
3) 2x 2 (2x 3)(3x 2)
4) 2x 2 (2x 3)(3x 2)
14a 6
10 Factor completely: 3t 3
5t 2
12t
1
ID: A
A2.A.7: Factoring Polynomials 1: Factor polynomial expressions completely using common
factor extraction, difference of perfect squares, quadratic trinomials
Answer Section
1 ANS: 4
2 ANS: 4
12x 4 10x 3
PTS: 2
12x 2
2x 2 (6x 2
REF: fall0917a2
5x 6)
PTS: 2
3 ANS:
(2x 1)(x 2)
REF: 061008a2
PTS: 2
4 ANS:
(4a 3)(a 3)
REF: 069503al
PTS: 2
5 ANS:
(3a 2)(a 1)
REF: 099503al
PTS: 2
6 ANS:
(5x 2)(2x 3)
REF: 069802al
PTS: 2
7 ANS:
(4a 5)(a 4)
REF: 090402al
PTS: 3
8 ANS:
(3x 4)(x 3)
REF: 010502al
PTS: 2
9 ANS:
2(2a 3)(3a 1)
REF: 030501al
PTS: 2
10 ANS:
t(3t 4)(t 3)
REF: 060502al
PTS: 2
REF: 010111siii
2x 2 (2x 3)(3x 2)
1
Regents Exam Questions A2.A.10: Fractional Exponents as Radicals Name: ________________________
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A2.A.10: Fractional Exponents as Radicals: Rewrite algebraic expressions with fractional
exponents as radical expressions
1 If x is a positive integer, 4x
2
1)
x
2) 2x
3) 4 x
1
4) 4
x
2 The expression x
1)
2
x5
2)
5
2
3)
4)
2
is equivalent to
2)
4
m3
x5
1
3)
5
m
4)
6
m5
b
3
b
n
n
2)
3
9 The expression (x
2
1)
2)
3
3)
4)
2
1
0, the expression
n
1)
8 Simplify: (16a b
5
6
2
3
is equal to
2
3
3
2
n2
n3
1
3
(x 2
1) 2
1
3
(x 2
1) 2
(x 2
1) 3
1
(x 2
1) 3
3
8a b )
0, is equivalent to
3
b
3)
4 If n
4
4
,b
m
4
2
x2
3
2
3
equivalent to
1
4)
1
2
7 When simplified, the expression
1
5
1
2
a6
6 Simplify:
m
x
a
5 Simplify:
3
2)
4)
is equivalent to
1)
3 The expression b
1
1)
2
3
b
3)
2
5
1
2
1)
2
3
1
3
is equivalent to
m
1
2
is
ID: A
A2.A.10: Fractional Exponents as Radicals: Rewrite algebraic expressions with fractional
exponents as radical expressions
Answer Section
1 ANS: 3
2 ANS: 4
x
2
5
REF: 060208b
1
x
2
5
1
5
x2
REF: 011118a2
3 ANS: 2
4 ANS: 3
5 ANS:
4
a
REF: 010413b
REF: 080807b
REF: 099414al
6 ANS:
a a
REF: 119411al
7 ANS: 4
8 ANS:
2ab
3
2ab 2
REF: 010617b
a3
REF: 069812al
9 ANS: 2
REF: 061011a2
1