Question

What is the simplified form of i^14

Answer 1

i^14
=((i^2)^7) i^2=-1
=(-1)^7
=-1

Answer 2

`i^(14)=-1`

Explanation:

The given expression is

`i^(14)`

We know that

`i^4=1`

Hence, on dividing 14 by 4 we get 3 as quotient and 2 as remainder. Hence, we can write the expressions as

`i^(14)\\\\=(i^4)^3\cdot i^2`

Now, use the values
`i^4=1,i^2=-1`

`(i^4)^3\cdot i^2\\\\=1^3\cdot (-1)\\\\=-1`

Therefore, the simplified form of the expression is -1