imaginary numbers. you can have a negative under the radical. you will bring out an “i“...
TRANSCRIPT
Imaginary
Numbers
1 i 1. 16
2. 81
3. 45
4. 200
You CAN have a negative under the radical. You will
bring out an “i“ (imaginary).
4i9i3 5i10 2i
Powers of i
(The i Chart)
“I one, I one!!”Negatives in the middle.
1
1
i
i
1
2
3
4
i
i
i
i
.25
.5
.75
0Reference
75
29
251
9536
5.
6.
7.
8.
i
i
i
i
Simplify
iii
1
Complex Number
Standard Form(add this to your
notes)
a bi
Add and Subtract Complex Numbers
Add/Subt Complex Numbers
1.Treat the i’s like variables2.Combine like terms3.Simplify (no powers of i
higher than 1 are allowed)
4.Answer in standard form a + bi
Simplify
9. (3 2 ) (7 6)i i
10 8i
Simplify
10. (6 5) (1 2 )i i 6 5 1 2i i 5 7i
Simplify
11. (9 4 ) (2 3 )i i
9 4 2 3i i 7 7i
Simplify
12. 9 (10 2 ) 5i i
9 10 2 5i i 1 7i
Simplify
4 3 4 313. (11 4 ) (2 6 )i i i i 4 3 4 311 4 2 6i i i i
9 10i
4 39 10i i 9 1 10 i
Multiplying Complex Numbers
(no powers of i higher than 1 are allowed in your answer)
Multiplying Complex Numbers
14. (3 )i i 23i i
3 ( 1)i 1 3i
Multiplying Complex Numbers
15. (2 3 )( 6 2 )i i 212 4 18 6i i i
12 22 6( 1)i 12 22 6i 6 22i
Multiplying Complex Numbers
16. 3 8 5i i 224 15 8 5i i i
24 7 5 1i 24 7 5i 29 7i
Dividing Complex Numbers
(no powers of i in the denominator are allowed in your answer)
What is a Conjugate?
Example: (2 – 4i)
17. Dividing – Multiply top & bottom by the Conjugate
3 42 4
ii
2 4
2 4
i
i
2
2
6 12 8 164 8 8 16
i i ii i i
6 20 16
4
1
116
i
10 20
20i
10 2020 20
i
12
i
18. Dividing – Multiply top & bottom by the Conjugate
ii
5 23 4
3 4
3 4
i
i
2
2
15 20 6 89 12 12 16
i i ii i i
15 26 8
9
1
116
i
7 26
25i
7 2625 25
i