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Transcript
```1.
You throw away the outside
and cook the inside.
Then you eat the outside
and throw away the inside.
What did you eat?:
corn
Check Homework
PRE
Lesson 3.4 & 3.5 Complex Number
& Complex Zeros
Objectives:
•To understand complex numbers.
•To add, subtract & multiply complex
numbers.
•To solve equations with complex
numbers as solutions.
To reduce a power
of i, just divide by 4
and the remainder
will correspond to
one of these.
i  1
2
i  1
3
i  i
4
i  1
i  1
13
Special care must be taken when performing
calculations involving square roots of negative
numbers. Although
when
a and b are positive. This is not true when
both are negative. For example:
1
9 x  54  0
54 54
2
9 x  54
2
9
9
x  6
x   6
2
x   6  1
x  i 6
2a. P( x)  x  x  x
x(x 2  x  1)
x 0
x2  x 1 0
3


x 0

2
1 i 3
x
2
2b. P( x)  x3  7 x 2  18 x  18; x  3

3 1 7 18 18

3 12 18
1


4
6
0
2
(x

3)
(x
 4 x  6)

  
x  3 x  2  i 2
   

2c. P( x)  x  x  2 x  2; x  1, 1
4
2
1 1
0 1
1 1
1 1 0
2 2
0 2
2 0
3
2
(x

1)
(x

x
 2)


  
1 1 1 0 2
   1
 2 2

1 2 2
0

2
(x
 2x  2)
(x

1)
(x

1)

  
 1 
x  1
x 
 i







Whenever a+bi is a zero, its
complex conjugate a-bi is also a zero:
3a. Degree 3 and zeros 2 and 3-i.
(x  2)(x  (3  i))(x  (3  i))



(x  2)(x  (3  i))(x  (3  i))


 


x 2
2 2

x 2 0
(x  2)


x  3i
(3 i) (3 i)
 x  (3  i)  0
x  (3  i)



3a. Degree 3 and zeros 2 and 3-i.
(x  2)(x  (3  i))(x  (3  i))
(x  2)(x  3 i)(x  3 i)





(x  2)(x 2  6x 10)

x 3  8x 2  22x  20
Classwork: Worksheet: 3.4 & 3.5
```
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