Explanation
- Define of Imaginary Number
[tex] \sqrt{ - 1} = i[/tex]
[tex] {i}^{3} = ( \sqrt{ - 1} )( \sqrt{ - 1} )( \sqrt{ - 1} )[/tex]
Because it is also defined that i² = -1. Therefore
[tex] {i}^{2} = - 1 \\ {i}^{3} = - 1 \sqrt{ - 1} [/tex]
We don't usually write 1 or -1. Simplify
[tex] {i}^{3} = - i[/tex]
Make sure to convert or simplify any negative numbers in square root in simplest form or with "i".
Answer
[tex] {i}^{3} = - i[/tex]
