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summary of this topic

Algebra of Complex Numbers

Algebra of Complex Numbers

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Power of i


 »  To calculate `i^n`

Remember `i^4 = 1` and `i^2=-1`. Quickly derive the following using this. No need to memorize

    →  express `n` in the form `n=4p+2q+r`, where `p,q, r in NN` natural numbers.

    →  `i^n = (-1)^q xx i^r`

Powers of `i`

plain and simple summary

nub

plain and simple summary

nub

dummy

To calculate `i^n`, use `i^4=1` and `i^2=-1`.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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The value of `i^n` for various values of n is discussed.


Keep tapping on the content to continue learning.
Starting on learning "Powers of i". ;;The value of i power n for various values of n is discussed.

What is the value of `i`?

  • `-1`
  • `sqrt(-1)`

The answer is '`sqrt(-1)`'

What is the value of `i^2`?

  • `-1`
  • `sqrt(-1)`

The answer is '`-1`'

It is defined that `i=sqrt(-1)`. Substitute that in the following
`i^2`
`quad quad = (sqrt(-1))^2`
`quad quad = (-1^(1/2))^2`
`quad quad = -1^(2/2)`
`quad quad = -1`

What is the value of `i^3`?

  • `-1`
  • `i`
  • `-i`

The answer is '`-i`'

`i^3`
`quad quad = i^(2+1)`
`quad quad = i^2 xx i^1`
`quad quad = -1 xx i`
`quad quad = -i`

What is the value of `i^4`?

  • `1`
  • `-1`

The answer is '`1`'

`i^4`
`quad quad = i^(2+2)`
`quad quad = (i)^2 xx i^2`
`quad quad = -1 xx -1`
`quad quad = 1`

What is the value of `i^0`?

  • `1`
  • `-1`
  • `i`

The answer is '`1`'

`i^0`
`quad quad = i^(1-1)`
`quad quad = i/i`
`quad quad = 1`

What is the value of `i^n`, if `n=4p+2q+r`?

  • `i`
  • `(-1)^q xx i^r`
  • `i^r`

The answer is '`(-1)^q xx i^r`'

`i^n`
`quad quad = i^(4p+2q+r)`
`quad quad = i^(4p) xx i^(2q) xx i^r`
`quad quad = (i^4)^p) xx (i^2)^q) xx i^r`
`quad quad = (-1)^q xx i^r`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Power of i: To calculate `i^n`, express `n` in the form `n=4p+2q+r`, where `p,q, r in NN` natural numbers. Then
`i^n = (-1)^q xx i^r`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is the value of `i^27`?

  • `1`
  • `-i`
  • `i`

The answer is '`-i`'

What is `i^20`?

  • `1`
  • `-1`
  • `i`
  • `-i`

The answer is '`1`'

What is `i^7`?

  • `1`
  • `-1`
  • `i`
  • `-i`

The answer is '`-i`'

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Progress

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Progress

What is the value of i ?
minus 1;-1
minus 1
square;root
square root of minus 1
The answer is 'square root of minus 1'
What is the value of i squared?
minus 1;-1
minus 1
square;root
square root of minus 1
The answer is ' -1 '
What is the value of i cube?
minus 1;-1
minus 1
i
i
minus i;-i
minus i
The answer is 'minus i'
What is the value of i power 4?
1
1
-1;minus 1
minus 1
The answer is ' 1 '
What is the value of i power 0?
1
1
-1;minus 1
minus 1
i
i
The answer is ' 1 '
What is the value of i power n if n equals 4p+2q+r?
i
i
minus
minus 1 power q multiplied i power r
i;power;r;are;or
i power r
The answer is 'minus 1 power q multiplied i power r'
To calculate i power n, use i power 4 equals 1 and i squared equals minus 1
Power of i: To calculate i power n, express n in the form 4p+2q+r, where p,q, r in whole numbers. Then ;; i power n = minus 1 power q multiplied by i power r .
What is the value of i power 27?
1
1
minus i
minus i
i
i
The answer is 'minus i'
What is the value of i power 20?
1
1
minus 1
minus 1
i
i
minus i
minus i
The answer is ' 1 '
What is i power 7?
1
1
minus 1
minus 1
i
i
minus i
minus i
The answer is 'minus i'

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