Carson Elementary And Intermediate Algebra 3e Page 4
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2
3
4M098
Carson Elementary and Intermediate Algebra 3e
Section 10.7
3. Raise i to powers.
Raising i to various powers leads to an interesting pattern:
i = 1 i = i
5
4
i
i
= i
2
6
4
i
2
i
= -1
i
= i
= (1)(-1) = -1
3
2
i = -1 i = -i
7
4
i
2
i = (1)(-1)i = -i
i
= i
i
= i
4
2
i
2
8
4
i
4
= 1 1 = 1
i
= i
= (-1)(-1) = 1
i
= i
A power of i can always be simplified to i, -1, -i or 1. Any power of i that is a multiple of 4 will simplify to 1.
41
Example 12:
i
i
4
10
The largest multiply of 4 less than 41 is 40.
(i
)
4
i
10
i
= 1
1
i
52
Example 13:
i
4
13
(i
)
The largest multiply of 4 less than or equal to 52 is 52.
13
4
1
i
= 1
1
45
Example 14:
i
1
45
i
The largest multiply of 4 less than 45 is 44.
1
11
4
i
i
4
i
= 1
1
i
Rationalize and simplify.
1
i
i
i
i
i
i
2
1
i
V. Zabrocki 2011
page 4
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