Bot GPT 4-o mini To simplify \( 3i[(2i) + (-3i - 5)] \) using the Distributive Property, follow these steps:
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Simplify inside the brackets: \[ -3i - 5 \text{ has no like terms to combine, so we can rewrite it as is.} \] Therefore: \[ (2i) + (-3i - 5) = 2i - 3i - 5 = -i - 5 \]
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Now apply the Distributive Property: \[ 3i[-i - 5] = 3i \cdot (-i) + 3i \cdot (-5) \]
- First, compute \( 3i \cdot (-i) \): \[ 3i \cdot (-i) = -3i^2 = -3(-1) = 3 \quad \text{(since } i^2 = -1\text{)} \]
- Next, compute \( 3i \cdot (-5) \): \[ 3i \cdot (-5) = -15i \]
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Combine the results: \[ 3 - 15i \]
The simplest form of \( 3i[(2i) + (-3i - 5)] \) is: \[ \boxed{3 - 15i} \]
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