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Powers of the Imaginary Unit>
Powers of the Imaginary Unit 2Powers of the Imaginary Unit 2
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Question 1 of 4
1. Question
Simplify
`i^(2006)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i^0=1`, `i^1=i`, `i^2=1` and `i^3=i`.Use the formula `i^(4n+r)` to simplify the powers of the imaginary unit.`i^(2006)` Divide the power `2006` by `4`. This gives `501` with a remainder of `2`. `=` `i^(4times501+2)` Rewrite using the formula `i^(4n+r)` where the `n=501` and the `r=2`. `=` `i^(501+\color(red)(2))` Simplify `i^(501+\color(red)(2))` The `2` means that this number is the same as `i^2=1`. `=` `1` `1` 
Question 2 of 4
2. Question
Simplify
`i^(995)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i^0=1`, `i^1=i`, `i^2=1` and `i^3=i`.Use the formula `i^(4n+r)` to simplify the powers of the imaginary unit.`i^(995)` Divide the power `995` by `4`. This gives `248` with a remainder of `3`. `=` `i^(4times248+3)` Rewrite using the formula `i^(4n+r)` where the `n=248` and the `r=3`. `=` `i^(992+\color(red)(3))` Simplify `i^(992+\color(red)(3))` The `3` means that this number is the same as `i^3=i`. `=` `i` `i` 
Question 3 of 4
3. Question
Simplify
`i^(222,002)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i^0=1`, `i^1=i`, `i^2=1` and `i^3=i`.Use the formula `i^(4n+r)` to simplify the powers of the imaginary unit.`i^(222,002)` Divide the power `222,002` by `4`. This gives `55,500` with a remainder of `2`. `=` `i^(4times55,500+2)` Rewrite using the formula `i^(4n+r)` where the `n=55,500` and the `r=2`. `=` `i^(222,000+\color(red)(2))` Simplify `i^(222,000+\color(red)(2))` The `2` means that this number is the same as `i^2=1`. `=` `1` `1` 
Question 4 of 4
4. Question
Simplify
`i^(780)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i^0=1`, `i^1=i`, `i^2=1` and `i^3=i`.Use the formula `i^(4n+r)` to simplify the powers of the imaginary unit.`i^(780)` Divide the power `780` by `4`. This gives `195` with a remainder of `0`. `=` `i^(4times195+0)` Rewrite using the formula `i^(4n+r)` where the `n=195` and the `r=0`. `=` `i^(780+\color(red)(0))` Simplify `i^(780+\color(red)(0))` The `0` means that this number is the same as `i^0=1`. `=` `1` `1`
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