Download 2.4 Complex Numbers

2.4
Complex Numbers
Standard form of a complex number
a + bi
Adding and Subtracting complex numbers
(3 – i) + (2 + 3i) =
2i + (-4 – 2i) =
3 - (-2 + 3i) + (-5 + i) =
5 + 2i
-4
-2i
Multiplying Complex numbers
Note: i2 = -1
(i)(-3i) = -3i2 = 3
(2 – i)(4 + 3i) = 8 + 6i – 4i – 3i2 = 11 + 2i
(3 + 2i)(3 – 2i) = 9 – 4i2 = 9 + 4 = 13
-6
Dividing Complex numbers
2  3i
4  2i
(4  2i)
8  4i  12i  6i

2
4  2i 
16  4i
2
2  16i
1 4
2 16i



  i
20 20
20
10 5
Note:
a i a
3 12  3i 12i  36i 2  -6
48  27  4 3i  3 3i  3i
1
 
2


3   1  3i  1  3i 
-3
1  3i  3i  3i 
2
 2  2 3i
Use the quadratic formula to solve
0 = 3x2 – 2x + 5
x
  2 
 2
23
2
 435
2   56
2  2 14i
x

6
6
1
14
 
i
3
3

i1 = i
i2 = -1
i3 =
i   i  -i
2 1
i4 = (i2)2 = (-1)2 = 1
  i i
i5 = i
2 2
What does i36 = (i2)18 = (-1)18 = 1
i53 =
(i )  i 
2 26
i