Question

If i=

`√( - 1)`
what is the value of

`{i}^(3)`
​

Answer 1

.......the answer is -1

Answer 2

Step-by-step explanation

• Define of Imaginary Number

`√( - 1) = i`

• Find the value of i³

`{i}^(3) = ( √( - 1) )( √( - 1) )( √( - 1) )`

Because it is also defined that i² = -1. Therefore

`{i}^(2) = - 1 \\ {i}^(3) = - 1 √( - 1)`

We don't usually write 1 or -1. Simplify

`{i}^(3) = - i`

Make sure to convert or simplify any negative numbers in square root in simplest form or with "i".

Answer

`{i}^(3) = - i`