Asked by blobby
Complex Numbers Unit Test
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Question
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)
Responses
15i
15 i
i15−−√
i start square root 15 end square root
3i5–√
Answers
Answered by
GPT-4o mini
To simplify the expression \((i \cdot \sqrt{5}) \cdot 3\) and show that the Associative Property of Multiplication holds true, you can rearrange the multiplication as follows:
\[
(i \cdot \sqrt{5}) \cdot 3 = i \cdot (\sqrt{5} \cdot 3) = i \cdot (3\sqrt{5})
\]
This yields:
\[
3\sqrt{5} i
\]
However, none of the given responses directly match \(3\sqrt{5} i\). Let's rewrite the response options to see if one of them can be equivalent or how they relate.
1. **15i**: This is \(15\) multiplied by \(i\), which does not match.
2. **\(i \sqrt{15}\)**: This doesn't match our expression either.
3. **\(3i \sqrt{5}\)**: This is actually equivalent to \(3\sqrt{5} i\) because multiplication is commutative.
Therefore, the correct answer that demonstrates the Associative Property of Multiplication for the given expression is:
**3i√5**.
\[
(i \cdot \sqrt{5}) \cdot 3 = i \cdot (\sqrt{5} \cdot 3) = i \cdot (3\sqrt{5})
\]
This yields:
\[
3\sqrt{5} i
\]
However, none of the given responses directly match \(3\sqrt{5} i\). Let's rewrite the response options to see if one of them can be equivalent or how they relate.
1. **15i**: This is \(15\) multiplied by \(i\), which does not match.
2. **\(i \sqrt{15}\)**: This doesn't match our expression either.
3. **\(3i \sqrt{5}\)**: This is actually equivalent to \(3\sqrt{5} i\) because multiplication is commutative.
Therefore, the correct answer that demonstrates the Associative Property of Multiplication for the given expression is:
**3i√5**.