Question

use the inverse relationship to complete the expression.
if ( i = sqrt{-1} ), then ( i^2 = \boxed{-1} ).
complete
using laws of exponents,
( i^3 = (i^2)i = )
done
( -i )
( -1 )
( 1 )
( i )

Explanation:

Step1: Recall \( i^2 \) value

We know \( i = \sqrt{-1} \), so \( i^2 = (\sqrt{-1})^2 = -1 \).

Step2: Calculate \( i^3 \)

Using exponent law \( a^m \cdot a^n = a^{m + n} \), \( i^3 = i^2 \cdot i \). Substitute \( i^2 = -1 \), we get \( i^3 = -1 \cdot i = -i \).

Answer:

\(-i\)