Download 1.3---multiply-imaginary

Daily Check
For the equation 4 x  8 x  4  0,
2
find the number of solutions using the
quadratic formula.
b  b  4ac
2a
2
Math I
Day 12 (8-25-09)
UNIT QUESTION: What is a
quadratic function?
Standard: MM2A3, MM2A4
Today’s Question:
How do we multiply complex
numbers?
Standard: MM2N1.c, d
1.3
Powers of i and
Multiplying Complex
Numbers
Since i  -1, then
i i
5
i  1
2
i  i
3
i 1
4
i  1
6
i  i
7
i 1
8
etc.
*For larger exponents,
divide the exponent by
4, then use the
remainder as your
exponent instead.
Example:
i ?
23
23
 5 with a remainder of 3
4
3
So, use i which  -i
i  i
23
Try These !
13
1. i
2. i
27
3. i
54
4. i
72
$25,000 Pyramid
$25,000 Pyramid
i
141
i
i
71
i
92
1
-i
i 45
i 54
i 63
i
-1
-i
i2
i3
i4
i14
-1
-i
1
-1
$25,000 Pyramid
i
173
i
i
82
i
95
-i
-1
i 35
i 66
i 77
-i
-1
i
i2
i3
i4
i 23
-1
-i
1
-i
Multiplying
Treat the i’s like variables, then change any that
are not to the first power
Ex:  i (3  i)
 3i  i 2
 3i  ( 1)
 1 3i
Ex: (2  3i )( 6  2i )
 12  4i  18i  6i 2
 12  22i  6(1)
 12  22i  6
 6  22i
Your Turn!
1) (3 i )(8  5i )
 29  7i
2) (4  3i)(4  3i)
 25
Your Turn!
3)  2i (1  4i )
 8  2i
4) (3  2i)(5  9i)
 33 17i
Conjugates:
Two complex numbers of the form a + bi and
a – bi are complex conjugates. The product is
always a real number
Ex: (2  4i)(2  4i)
 4  8i  8i  16i 2
 4  16(1)
 20
Practice
Workbook Page 14
Assignment
Page 13 #1-25 (odd)
Also, find the value for
each of the following:
i45
i52
i25
i74
i91
i102