Square roots of numbers are called numbers. Unit Imaginary Number i is a number whose square is -1....
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7.9 Complex Numbers
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Transcript of Square roots of numbers are called numbers. Unit Imaginary Number i is a number whose square is -1....
7.9 Complex Numbers
• Square roots of numbers are called numbers.
• Unit Imaginary Number• i is a number whose square is -1. That is,
• In other words, . i2 1
i 1
negativeimaginary
1. Find the pattern. • a. d.
• b. e. • c. f.
• d. g.
• Pattern?
i1
2i
3i
4i
5i
6i
7i
8i
• So, to calculate any high power of i, you can convert it to a lower power by taking the closest multiple of 4 that's no bigger than the exponent and subtracting this multiple from the exponent.
• Example: i99 i963 i 424 3 i3 i
Simplify.
2.
3.
4.
i17
i120
i64,002
Theorem• For every positive real number r,
r i r
Express in simplest form as a real number or a pure imaginary number.
• 5.
• 6.
• 7.
50
3 75
9
7
Express each of the following in simplest form.
8.
9.
10.
3 75
2 12 5 6
49 12
Express each of the following in simplest form.
11.
12.
3 7 4 175
300 192
• Remember, i is still a square root. So, we cannot have i left in the and we must rationalize!
denominator
Express each of the following in simplest form.
• 13.
• 14.
6
i3
5
2i
Express each of the following in simplest form.
• 15.
• 16.
7 63 4i
7
6
