Apply the Distributive Property to show 3i[(2i)+(-3i-5)] in its simplest form. (1 point) □ +□ i

Answer 1

To simplify the expression \( 3i[(2i) + (-3i - 5)] \) using the Distributive Property, we start with the expression inside the brackets.

1. Simplify the expression inside the brackets: \[ 2i + (-3i - 5) = 2i - 3i - 5 = -1i - 5 = -i - 5 \]

2. Now substitute this back into the original expression: \[ 3i[-i - 5] \]

3. Apply the Distributive Property: \[ 3i \cdot (-i) + 3i \cdot (-5) \]

4. Calculate each term:

   • First term: \[ 3i \cdot (-i) = -3i^2 \] Recall that \( i^2 = -1 \), therefore: \[ -3i^2 = -3(-1) = 3 \]

   • Second term: \[ 3i \cdot (-5) = -15i \]

5. Combine the results: \[ 3 - 15i \]

Now, we express the answer in the form of \( a + bi \): \[ 3 - 15i \]

Thus, in the form \( \boxed{3} + \boxed{-15} i \).