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The Imaginary Unit
i 1
52 x5x
5ix
92 x9x
ix 3
Jeff Bivin -- LZHS
51x 91x
More about Imaginary Numbers
1i
1122 i
iiiii 123
1)1)(1(224 iii
iiiii ))(1(45
1)1)(1(246 iii
iiiii ))(1(347
1)1)(1(448 iii
iiiiii )1)(1(449
1)1)(1)(1(24410 iiiiiiiiii ))(1)(1(34411
1)1)(1)(1(44412 iiiiJeff Bivin -- LZHS
This is fun!
iiiiiiiii ))(1)(1)(1)(1)(1(34444423
iiiii )()1( 535423
iiiii )()1( 1010441
1)1()1( 18218474 iii
1)1()1( 302304122 iii
Jeff Bivin -- LZHS
Complex Numbers
For any real numbers a and b, the number
a + bi
is a complex number.
Examples:
i23 i52
31 i
52 ii7
Jeff Bivin -- LZHS
11
15,7
4,2
1
3 7
2
53
1152
i
i3
2i
325 i
i27
Jeff Bivin -- LZHS
Addition & Subtraction
iii 98)75()23(
iii 63)92()35(
iii 10)52()68(
Example 1
Example 2
Example 3
Jeff Bivin -- LZHS
Multiplication
21081512)54()23( iiiii
1081512 ii
i232
23515146)73()52( iiiii )1(3515146 ii
i 41
)1(1081512 ii
3515146 ii
Example 1
Example 2
Jeff Bivin -- LZHS
Graphing Complex Numbers
i23 i54 i23 i34
i32
Jeff Bivin -- LZHS
Solve using the Quadratic Formulax2 + 6x + 13 = 0
a = 1b = 6c = 13
a
acbbx 2
42
12
131466 2
x
2
52366 x
2166 x
246 ix
Jeff Bivin -- LZHS
2)23(2 i i23
Solve using the Quadratic Formula3x2 + 7x + 5 = 0
a = 3b = 7c = 5
a
acbbx 2
42
32
53477 2
x
6
60497 x
6117 x
6117 ix
Jeff Bivin -- LZHS
Solve using the Quadratic Formula3x2 - 2x + 5 = 0
a = 3b = -2c = 5
a
acbbx 2
42
32
534)2(2 2
x
6
6042 x
6562 x
61422 ix
Jeff Bivin -- LZHS
6)141(2 i 3
141 i
