A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Algebra 2
Ch.5 Notes Page 23
P23 5­6 Complex Numbers
Aug 19­6:20 AM
a. d. b. c. e. f. Feb 10­7:14 AM
1
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
What are the subsets of the set of complex numbers?
Number Systems
Natural 1,2,3
Whole
0,1,2,3
Integers
­1,0, 1
Rational
a/b (b ≠ 0)
Irrational
√2, π, ­√3
Real
Imaginary
Complex
All Rational and Irrational
i, ­3i, 2i, i √5
All Real and Imaginary (a + bi)
Oct 14­8:33 AM
Complex Numbers
Any Number of the form a + bi
a and b are real. i is imaginary.
5 + 4i
Oct 21­1:03 PM
2
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Feb 10­7:19 AM
Imaginary Numbers
√­1 = i
√­1 = i
2
(√­1) = ­1
(√­1)3 = ­i
4
(√­1) = 1
Sep 22­9:21 AM
3
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Feb 10­7:19 AM
Feb 10­7:19 AM
4
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Feb 10­7:14 AM
Feb 10­7:14 AM
5
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Feb 10­7:21 AM
Work with a partner. Use the definition of the imaginary unit i to match each quadratic equation with its complex solution. Justify your answers.
a. x2 − 4 = 0 b. x2 + 1 = 0 c. x2 − 1 = 0
d. x2 + 4 = 0 e. x2 − 9 = 0 f. x2 + 9 = 0
Feb 10­7:14 AM
6
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Feb 10­7:21 AM
Finding Complex Solutions
3x2 + 48 = 0
­5x2 ­ 150 = 0
Oct 14­8:36 AM
7
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
Finding Absolute Values
Distance from the Origin on the complex number plane.
Use the Pythagorean Theorem.
Complex Number Plane
3 + ­4i
Oct 14­8:27 AM
Additive Inverse
Distribute a ­1 through the entire Complex Number
Example:
­2 + 5i
Find the Additive Inverse:
4 ­ 3i
2 + ­5i
Oct 14­8:35 AM
8
A2_3.2Pilot5.6Notes.notebook
February 12, 2016
HW #24
3.2 P108 #5,6,9,10,21­24,37­40,44,55­58
Please put your name and class period at the top of the homework. Also include the homework number.
Aug 19­6:25 AM
9