Complex Numbers Unit Test

Question

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

Answer 1

To simplify \( 3i[(2i) + (-3i - 5)] \) using the Distributive Property, follow these steps:

1. Simplify inside the brackets: \[ -3i - 5 \text{ has no like terms to combine, so we can rewrite it as is.} \] Therefore: \[ (2i) + (-3i - 5) = 2i - 3i - 5 = -i - 5 \]

2. 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 \( 3i \cdot (-5) \): \[ 3i \cdot (-5) = -15i \]

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

The simplest form of \( 3i[(2i) + (-3i - 5)] \) is: \[ \boxed{3 - 15i} \]