A2M1L37-SB Imaginary Numbers Part 1.notebook

A2M1L37­SB Imaginary Numbers Part 1.notebook
Imaginary Numbers
Standards: N­CN.A.1
N­CN.A.2
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Solve each equation for x: 1) x­1 = 0 2) x + 1 = 0 3) x2 ­ 1= 0 4) x2 + 1= 0
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Imaginary Numbers
the imaginary unit
represents
√ -1
i
Practice using the imaginary unit by
simplifying the following:
i = √-1
A2M1L37­SB Imaginary Numbers Part 1.notebook
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Whole
Numbers
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Integers
...-3,-2,-1,0,1,2,3...
Whole
Numbers
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Rational Numbers
(integers plus fractions)
Integers
...-3,-2,-1,0,1,2,3...
Whole
Numbers
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Rational Numbers
(integers plus fractions)
Integers
...-3,-2,-1,0,1,2,3...
Irrational
Numbers
(non-repeating,
Whole
non-terminal
Numbers
decimals)
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Real Numbers
Rational Numbers
(integers plus fractions)
Integers
...-3,-2,-1,0,1,2,3...
Irrational
Numbers
(non-repeating,
Whole
non-terminal
Numbers
decimals)
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Real Numbers
Rational Numbers
(integers plus fractions)
Integers
...-3,-2,-1,0,1,2,3...
Irrational
Imaginary
Numbers
Numbers
(non-repeating,
Whole
non-terminal
Numbers
decimals)
0,1,2,3...
Counting
Numbers
1,2,3...
√-1
A2M1L37­SB Imaginary Numbers Part 1.notebook
Complex Numbers
(real + Imaginary)
Real Numbers
Rational Numbers
(integers plus fractions)
Integers
...-3,-2,-1,0,1,2,3...
Irrational
Numbers
(non-repeating,
Whole
non-terminal
Numbers
decimals)
0,1,2,3...
Counting
Numbers
1,2,3...
November 10, 2015
Examples of Complex numbers 2­3i, 5+ 8i, ­7+2i, 16 ­ 9i
Imaginary
Numbers
√-1
3i, 5i, -2i
A2M1L37­SB Imaginary Numbers Part 1.notebook
Complex numbers 6+3i 4 + 0i
0 + 3i ­2 + 5i November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Solve using the quadratic formula
1. x2 + 9 = 0 2. x2 + 4x + 8 = 0
A2M1L37­SB Imaginary Numbers Part 1.notebook
Plot
i
1) 4i
i
2)­3i
i
3) 4+5i
i
4) ­2­3i
i
5) ­1+4i
i
i
i
i
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
R90
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Powers of i
0
i =
i1 =
2
i =
i3 =
i4 =
5
i =
6
i =
i7 =
i8 =
i9 =
i10 =
i11 =
i12 =
13
i =
i14 =
15
i =
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Procedure for Simplifying Powers of i
Example: Simplify i35
1) Divide the exponent by 4.
2) Use the remainder as the
new exponent.
3) Write in a + bi form i35 = ­i
8 R3
4 35
32
3
i3
0 + ­i or ­i
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Division by 4 and the
possible remainders ­
Remainder of 0 = .0
Remainder of 1 = .25
Remainder of 2 = .5
Remainder of 3 = .75
A2M1L37­SB Imaginary Numbers Part 1.notebook
November 10, 2015
Write in a + bi form:
40
1)
i
2)
i53
3)
i18
4) i2003
A2M1L37­SB Imaginary Numbers Part 1.notebook
Review: November 10, 2015
A2M1L37­SB Imaginary Numbers Part 1.notebook
Homework Worksheet
November 10, 2015