Complex Numbers 2010 September 15, 2010
A.6 Complex and Imaginary Numbers
Objectives
What is an imaginary number?
What is a complex number?
Jan 30­10:53 AM
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Complex Numbers 2010 September 15, 2010
Warm­up: Solve using the quadratic formula.
­5x2 + 12x ­ 8 = 0
6 ± 2i
x = 5 Sep 14­1:06 PM
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Complex Numbers 2010 September 15, 2010
What is an imaginary number?
Remember, up to this point, we could not take the
square root of a negative number.
Now, an imaginary unit is defined as follows:
i = ­ 1
and
i2 = ­ 1
4
i = 1
3
i = ­i
Jan 30­11:00 AM
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Complex Numbers 2010 September 15, 2010
The square root of a negative number is defined as follows:
­ a = i a
when a > 0
So, try these!
1. ­ 33 = 3. ­ 50 = 2. ­ 81 =
4. ­ 12 =
Jan 30­11:05 AM
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Complex Numbers 2010 September 15, 2010
Sep 15­12:43 PM
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Complex Numbers 2010 September 15, 2010
A complex number is in the form a + bi, where a and b are real numbers and i is the imaginary unit ­ 1 .
Complex Numbers
3 + 2i
2 + 4i
real numbers
b = 0
­ 4 ­ i 7
pure imaginary numbers
a = 0
i 2i i 7
0 ­4 3 Jan 30­11:12 AM
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Complex Numbers 2010 September 15, 2010
Simplify:
1. (9i)(3i)
2. (­4i)(5i)
2. (2 + 6i) ­ (1 ­ 3i) 3. (5 + 7i)(4 + 8i) Jan 30­3:34 PM
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Complex Numbers 2010 September 15, 2010
Homework
Complex Numbers Worksheet
Jan 30­3:38 PM
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