To apply the Distributive Property to the expression \(3i[(2i) + (-3i - 5)]\), we first simplify the expression inside the brackets.
-
Simplify the expression inside the brackets: \[ (2i) + (-3i - 5) = 2i - 3i - 5 = -i - 5 \]
-
Rewrite the expression: \[ 3i[-i - 5] \]
-
Apply the Distributive Property: \[ 3i \cdot (-i) + 3i \cdot (-5) \]
-
Calculate each term:
-
For the first term: \[ 3i \cdot (-i) = -3i^2 \] Since \(i^2 = -1\), we have: \[ -3i^2 = -3(-1) = 3 \]
-
For the second term: \[ 3i \cdot (-5) = -15i \]
-
-
Combine the results: \[ 3 - 15i \]
So, the expression \(3i[(2i) + (-3i - 5)]\) in its simplest form is: \[ \boxed{3 - 15i} \]