Which of the following is equivalent to the expression (i⋅5–√)⋅3 , which shows that the Associative Property of Multiplication holds true for complex numbers?(1 point)

Question

Responses

i15−−√
i start square root 15 end square root

3i5–√
3 i start square root 5 end square root

i⋅(5–√⋅3)
i times left parenthesis start square root 5 end square root times 3 right parenthesis

15i

Answer 1

To determine which expression is equivalent to \((i \cdot \sqrt{5}) \cdot 3\), let's simplify the given expression step by step.

We start with: \[ (i \cdot \sqrt{5}) \cdot 3 \]

According to the Associative Property of Multiplication, we can group the factors in any way without changing the product. That means we can rewrite the expression as: \[ i \cdot (\sqrt{5} \cdot 3) \]

Now, let's simplify this further: \[ i \cdot (\sqrt{5} \cdot 3) = i \cdot (3\sqrt{5}) = 3i \cdot \sqrt{5} \]

So, the expression \( (i \cdot \sqrt{5}) \cdot 3 \) is equivalent to \( 3i \cdot \sqrt{5} \).

Now, we can match this with the options provided:

1. \( i \sqrt{15} \)
2. \( 3i \sqrt{5} \)
3. \( i \cdot (\sqrt{5} \cdot 3) \)
4. \( 15i \)

The option that corresponds with our simplified expression \( 3i \cdot \sqrt{5} \) is: \( 3i \sqrt{5} \)

So the answer is: 3i√5