Question

Power of i and there multiplicative inverse

Answer 1

The multiplicative inverse of power of i are:

• 'i' is '-i'

• 
  `i^(2)` is '-1'

• 
  `i^(3)` is 'i'

• 
  `i^(4)` is '1'

• 
  `i^5` is '-i'

Explanation:

'i' is a complex number with the property such that:

`√(-1)=i`

`i^2=-1\\\\i^3=-i\\\\i^4=1\\\\i^5=i\\\\i^6=i^2=-1\\\\i^7=-i`

and so on.

" In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1"

The multiplicative inverse of :

• 'i' is '-i'

since
`i*-i=-i^2=-(-1)=1`

• 
  `i^(2)` is '-1'

since
`i^2=-1\\\\-1*-1=1`

• 
  `i^(3)` is 'i'

since
`i^3=-i\\\\-i*i=-i^2=-(-1)=1`

• 
  `i^(4)` is '1'

since
`i^4=1\\\\1*1=1`

• 
  `i^5` is '-i'

since
`i^5=i\\\\i*-i=-i^2=-(-1)=1`