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