warm up. questions over hw? skills check simplify
TRANSCRIPT
1 i
1. 36
2. 96
3. 325
4. 612
6i4 6i5 13i6 17i
Warm up
Questions over hw?
Skills Check
Simplif
y.
4
3 6
208
1. 18
2. 64
3. 27
4. 2 4
5. 3 450
d
x y
k
Powers of iand Complex Operations
“I one, I one!!”Negatives in the middle.
1
1
i
i
1
2
3
4
i
i
i
i
.25
.5
.75
0
13
27
54
72
5.
6.
7.
8.
i
i
i
i
Try these!
Add and Subtract Complex Numbers
Add/Subt Complex Numbers
1.Treat the i’s like variables2.Combine the real parts
then combine the imaginary parts
3.Simplify (no powers of i higher than 1 are allowed)
4.Write your 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
11 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
111 4 2 1 6i i
9 10i
Multiplying Complex Numbers
Multiplying Complex Numbers
1.Treat the i’s like variables
2.Simplify all Powers of i higher than 1
3.Combine like terms4.Write your answer in
standard form a + bi
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 15 8 5 1i i 24 7 5i 29 7i
Dividing Complex Numbers
What is a Conjugate?
17. Dividing – Multiply top & bottom by the Conjugate
5 23 8
ii
3 8
3 8
i
i
2
2
15 40 6 169 24 24 64
i i ii i i
115 40 6 16
9 24 24 4 16
i i
i i
30 4673
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 20 6 8
9 12 1 116
1
2
i i
i i
7 2625
i
7 2625 25
i
CW/HWComplex Numbers – Practice Worksheet