imaginary numbers essential question: how do we take the square root of negative numbers?
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Imaginary Numbers
Essential Question:How do we take the square root of negative numbers?
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i1i
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• You can't take the square root of a negative number, right?
• When we were young and still in Algebra I, no numbers that, when multiplied by themselves, gave us a negative answer.
• Squaring a negative number always gives you a positive. (-1)² = 1. (-2)² = 4 (-3)² = 9
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So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary”
1i
So, does
1really exist?
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Examples of how we use
1i
16 16 1
4 i 4i
81 81 1
9 i 9i
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i
i
i
i
1i
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Ex: Solve x2+ 6x +10 = 0
aacbbx
242
a = 1b = 6c = 10
26 6 4 1 102 1
1st
6 36 4 1 102 1
2nd 6 36 402
6 42
6 22i
6 2 6 2
2 2i iand
3 3i and i
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Ex: Solve x2+ 3x +5 = 0
aacbbx
242
a = 1b = 3c = 5
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Assignment
TEXT p.206(1 – 4, 30 – 33)