Chapter 15 Study Guide
Name:__________________________
1. Give a definition & at least two examples of values that would exist in each of the following number systems.
Natural ℕ:
Whole 𝑾:
Integers ℤ:
Rational ℚ:
Irrational ⅉ:
Real ℝ:
Imaginary I:
Complex ℂ:
2. Name all the systems to which each of the following numbers would belong.
𝟏𝟕
𝟑
a) −𝟏𝟓
b)
e) √𝟐
̅
f) . 𝟗
c) 𝟐𝝅
d) 0
g) 𝟔𝒊
h) 𝟑 + 𝟐𝒊
3. Given each number system decide if they are closed for Addition, Subtraction, Multiplication, and Division
Natural ℕ:
Imaginary I:
Integers ℤ:
4. Rewrite each of the following repeated decimals as a simplified fraction.
̅
a) . 𝟑
̅̅̅̅
b) . 𝟏𝟗
̅̅̅̅̅̅
c) . 𝟑𝟐𝟒
̅̅̅̅
d) . 𝟖𝟐
̅
e) . 𝟗
f) . ̅̅̅̅
𝟗𝟑
g) . ̅̅̅̅̅̅̅̅̅
𝟏𝟐𝟑𝟒𝟓
h) . ̅̅̅̅
𝟐𝟕
5. Identify the property being used in each of the problems
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
6. Calculate each power of 𝒊.
a)
b)
c)
d)
e)
i)
j)
k)
l)
m)
7. Simplify each expression using 𝒊 (write all answers as a complex number if needed)
a)
f)
b)
c)
d)
g)
h)
i)
8. Simplify each expression as much as possible. (write all answers as a complex number if needed)
a)
b)
c)
e)
f)
g)
d)
h)
9. Determine the real and the imaginary part of each complex number 𝒂 + 𝒃𝒊.
a)
b)
c)
d)
10. Find the complex conjugate for each of the following and then multiply them together.
a)
b)
c)
e)
f)
11. Calculate each quotient.
a)
b)
c)
d)
e)
f)
12. Determine the number of roots/zeros and decide if they are real or imaginary.
13. Find the zeroes for each of the following functions
a)
b)
d)
c)
e)
22) Factor each of the following
a) 𝒙𝟐 − 𝟏𝟏𝒙 − 𝟒𝟐
b) 𝟐𝒙𝟐 + 𝟑𝒙 − 𝟐𝟎
c) 𝟐𝒑𝟑 + 𝟓𝒑𝟐 + 𝟏𝟎𝒑 + 𝟐𝟓
d) 𝒙𝟐 − 𝟔𝒙 − 𝟐
e) 𝒙𝟐 + 𝟏𝟎𝒙 + 𝟐𝟓
f) 𝒙𝟐 − 𝟗