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