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

Answer 1

To simplify the expression \( 3i[(2i) + (-3i - 5)] \), we'll use the Distributive Property. This property states that \( a(b + c) = ab + ac \).

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

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

3. Now, distribute \( 3i \) to both terms inside the brackets: \[ 3i \cdot (-i) + 3i \cdot (-5) \]

4. Calculate each term:

   • For \( 3i \cdot (-i) \): \[ = -3i^2 \] Since \( i^2 = -1 \), this becomes: \[ = -3(-1) = 3 \]

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

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

The simplest form of the expression \( 3i[(2i) + (-3i - 5)] \) is: \[ 3 - 15i \]

So the correct final answer is \( \boxed{3 - 15i} \).