Which of the following is equivalent to the expression (i· 5-sqrt())· 3 which shows that the Associative Property of Multiplication holds true for complex numbers? (1 point) 15 3isqrt(5) vector i· (sqrt(5)-3) isqrt(15)

Answer 1

To check whether the Associative Property of Multiplication holds true for the expression \((i \cdot (5 - \sqrt{3})) \cdot 3\), we can evaluate it step by step:

1. Original Expression: \((i \cdot (5 - \sqrt{3})) \cdot 3\)

2. Using the Associative Property: We can rewrite this as: \[ i \cdot ((5 - \sqrt{3}) \cdot 3) \]

3. Multiply inside the parentheses: \[ (5 - \sqrt{3}) \cdot 3 = 15 - 3\sqrt{3} \]

4. Now substitute it back into the expression: \[ i \cdot (15 - 3\sqrt{3}) \]

5. Distribute \(i\): \[ i \cdot 15 - i \cdot 3\sqrt{3} \]

So, the entire expression becomes: \[ 15i - 3i\sqrt{3} \]

Thus, the equivalent expression is \(15i - 3i\sqrt{3}\).

Now, let's examine the options again:

• 15 (incorrect)
• \(3i\sqrt{5}\) (incorrect)
• \(i \cdot (\sqrt{5} - 3)\) (incorrect)
• \(i\sqrt{15}\) (incorrect)

None of those options match the derived result of \(15i - 3i\sqrt{3}\).

Therefore, if you want to check which option that was given might've been equivalent originally, or if there was a misunderstanding in the expression itself. But as per standard calculation, the result we've derived accurately shows the Associative Property of Multiplication for this expression involving complex numbers.

Please verify if the expressions given match your context or if there's an error in transcription.