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5.6 Complex Numbers
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Solve the following quadratic:
x2 + 1 = 0
Is this quadratic factorable?
What does its graph look like?
x 2 1
x 2 1
x 1
But I thought that you could not take the square root of a negative number???
1ii is called an imaginary number because many thought that the square root of an imaginary number was impossible.
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Complex Numbers
Complex numbers are the combination of real numbers and imaginary numbers.
Complex numbers are written in the form:
a bi
Real Part
Imaginary Part
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Simplifying Complex Numbers
16 i4
32 24 i24
216 i66
150 i65
1002 i20
2002 i220
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Simplifying Complex Numbers
5 16
5 4 1
5 4i
32 7
7 4 2
7 4 2i
108 6
6 6 3i
75 25
25 5 3i
273752 ii 39310 i319
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Solve the quadratic equation
23 10 26x
363 2 x122 x
122 x
12ix
32ix
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Adding and Subtracting(add or subtract the real parts, then add or
subtract the imaginary parts)
Ex: )33()21( ii )32()31( ii
i52
Ex: )73()32( ii )73()32( ii
i41
Ex: )32()3(2 iii )32()23( iii
i21
Ex: )3( ii 23 ii )1(3 i
i31
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Multiplying complex numbers
Simplify the following:
3 2i 4 5i
12 15i 8i 10i2
110712 i
12 7i 10
22 7i
5 7i 2 3i
10 15i 14i 21i2
1212910 i 212910 i
i2911
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Multiplying complex numbers
Simplify the following:
3 i 2
9 6i i2
8 6i
5 7i 5 7i
25 49i2
25 4974