Topics
>
Precalculus>
Complex Numbers>
Powers of the Imaginary Unit>
Powers of the Imaginary Unit 2Powers of the Imaginary Unit 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
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`
Quizzes
- Simplify Roots of Negative Numbers 1
- Simplify Roots of Negative Numbers 2
- Powers of the Imaginary Unit 1
- Powers of the Imaginary Unit 2
- Solve Quadratic Equations with Complex Solutions 1
- Solve Quadratic Equations with Complex Solutions 2
- Equality of Complex Numbers
- Add and Subtract Complex Numbers 1
- Add and Subtract Complex Numbers 2
- Multiply Complex Numbers 1
- Multiply Complex Numbers 2
- Divide Complex Numbers
- Complex Numbers – Product of Linear Factors 1
- Complex Numbers – Product of Linear Factors 2
- Mixed Operations with Complex Numbers