Select the correct property of complex numbers that justifies each step to simplify the expression (12 + 2i) - (-2 + 3i).(5 points)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.(12 + 2i) - (-2 + 3i)12 + 2i + 2 - 3i12 + 2 + 2i - 3i(12 + 2) + (2i - 3i)14 - i

Question

distributive property, the simplified expression, commutiative property, the given expression or associative property match all 5

Answer 1

Let's break down the steps of simplifying the expression \((12 + 2i) - (-2 + 3i)\) and identify the correct property of complex numbers that justifies each step.

1. Step: \((12 + 2i) - (-2 + 3i)\)
   Property: The given expression

2. Step: \(12 + 2i + 2 - 3i\)
   Property: Distributive property (distributing the negative sign)

3. Step: \(12 + 2 + 2i - 3i\)
   Property: Commutative property (rearranging terms)

4. Step: \((12 + 2) + (2i - 3i)\)
   Property: Associative property (grouping terms)

5. Step: \(14 - i\)
   Property: The simplified expression

So, inserting the responses into their corresponding inputs would result in:

1. The given expression
2. Distributive property
3. Commutative property
4. Associative property
5. The simplified expression