To determine which expression is equivalent to \((i \cdot \sqrt{5} - \sqrt{3})\) and shows the Associative Property of Multiplication holds true for complex numbers, we can simplify the expression step by step.
The expression given is \(i \cdot \sqrt{5} - \sqrt{3}\). We can also consider the Associative Property in the context of complex multiplication, which states that \((a \cdot b) \cdot c = a \cdot (b \cdot c)\) for any numbers \(a\), \(b\), and \(c\).
Now let's check the response options:
- \(i \sqrt{15}\): This does not represent the original expression correctly.
- \(i \cdot (\sqrt{5} \cdot 3)\): While this uses multiplication, it changes the expression, as \(\sqrt{5} \cdot 3\) does not equal \(\sqrt{5} - \sqrt{3}\).
- \(15i\): This is simply a constant multiplied by the imaginary unit \(i\), which does not reflect our original expression.
- \(3i \sqrt{5}\): This also changes the original expression.
Given these options, it's clear the goal is to use the associative property correctly, but none of the provided responses give an equivalent expression to what was originally stated \((i \cdot \sqrt{5} - \sqrt{3})\).
The closest interpretation considering error and associated factors might be \(i \cdot \sqrt{5} - \sqrt{3}\) not being reinterpreted soundly in the options provided, as all seem to deviate in representation.
Hence, it appears none of the provided options correctly represents the original expression neither does it illustrate the associative property if association is mistakenly abstracted.
In conclusion, based on the responses, none of the options directly corresponds as equivalent to \((i \cdot \sqrt{5}) - \sqrt{3}\).
1 answer