Ex: Solve x2+ 6x +10 = 0

a

acbbx

2

42

a =

b =

c =

26 6 4 1 10

2 1

1st

6 36 4 1 10

2 1

2nd 6 36 40

2

6 4

2

6 2

2

i

6 2 6 2

2 2

i iand

3 3i and i

Solve x2+ 7x +14 = 0

a

acbbx

2

42

a =

b =

c =

27 7 4 1 14

2 1

1st

7 49 4 1 14

2 1

2nd 7 49 56

2

7 7

2

7 7

2

i 7 7

2 2

i

Questions on any previous hw?

Graphing in Graphing in thethe

Complex PlaneComplex Plane

The Complex PlaneThe Complex Plane

Graphing in the complex plane

i34 .

i52 .i22 .

i34

.

Absolute Value of a Complex Number

• The distance the complex number is from the origin on the complex plane.

• If you have a complex number (a + bi)

the absolute value can be found using:

22 ba

Find the absolute value of the complex number.1. 15 + 8i 15 8i

2 215 8

17

Find the absolute value of the complex number.2. -5 + 6i 5 6i

2 25 6

61

Find the absolute value of the complex number.3. -2 – 4i 2 4i

2 22 4

2 5

Find the absolute value of the complex number.3. 9i 0 9i

2 20 9

9

Examples

1. i52

22 )5()2(

254 29

2. i622 )6()0(

360

366

Which of these 2 complex numbers is closest to the origin (smallest distance)?

-2+5i

Try These!!!

1. 4 i

2 2(4) ( 1)

16 1 17

2. 3i2 2(0) (3)

0 9

93

Which of these 2 complex numbers is closest to the origin? 3i

Assignment

p.19 #1 – 17

p. 20 #1 – 8

p.94 #8, 10