Question

If i is raised to an odd power, then it can not simplify to be

1. -1

2. -i

3. i

Answer 1

-1

Explanation:

If i is raised to an odd power, then it can not simplify to be

-1

-i

i

Odyssey

Answer 2

1. -1

Explanation:

Since we know that i is an imaginary number. We also know that
`i=√(-1)` and
`i^2=-1`.

Let us see i raised to different powers.

`i^3=i^2\cdot i`

`i^3=-1\cdot i`

`i^3=-i`

`i^4=i^2\cdot i^2`

`i^4=-1\cdot -1`

`i^4=1`

`i^5=i^4\cdot i`

`i^5=1 \cdot i`

`i^5= i`

`i^6=i^4\cdot i^2`

`i^6=1 \cdot -1`

`i^6=-1`

`i^7=i^4\cdot i^3`

`i^7=1\cdot -i`

`i^7=-i`

`i^8=i^4\cdot i^4`

`i^8=1\cdot 1`

`i^8=1`

`i^9=i^5\cdot i^4`

`i^9=i\cdot 1`

`i^9=i`

We can see that when we raise i to 3rd power and 7th power we got -i and when we raised i to 5th and 9th power we got i.

Therefore, if we raise i to an odd power, it can not simplify to be -1 and 1st option is the correct choice.