Question

If i=sqr-1, what is the value of i^3?
-1
i
1
-i

Answer 1

After solving we get
`\mathbf{i^3=-i}`

Option D is correct.

Explanation:

We are given:

If
`i=√(-1)` we need to find the value of
`i^3`

Solving:

`i=√(-1)`

Taking cube on both sides

`i^3=(√(-1))^3\\`

We can write
`a^3= a^2.a^1` Using this for solving:

`i^3=(√(-1))^2.(√(-1))\\We \ know \ (√(-1))^2 =- 1 \ and \ √(-1)=1 \\i^3=-1(i)\\i^3=-i`

So, after solving we get
`\mathbf{i^3=-i}`

Option D is correct.