Question

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

Answer 1

To demonstrate the Associative Property of Multiplication with the expression \((i \cdot 5) \cdot 3\), we'll show that it is equivalent to \(i \cdot (5 \cdot 3)\).

1. **Calculate \((i \cdot 5) \cdot 3\):**
\[
(i \cdot 5) \cdot 3 = i \cdot (5 \cdot 3) = i \cdot 15
\]

2. **Calculate \(i \cdot (5 \cdot 3)\):**
\[
5 \cdot 3 = 15 \quad \text{(first do the multiplication)}
\]
\[
i \cdot (5 \cdot 3) = i \cdot 15
\]

Now, both calculations yield the same result:
\[
(i \cdot 5) \cdot 3 = i \cdot 15
\]
\[
i \cdot (5 \cdot 3) = i \cdot 15
\]

Thus, both forms are equal, proving that the Associative Property of Multiplication holds true for complex numbers.

The expression \((i \cdot 5) \cdot 3\) is equivalent to \(i \cdot (5 \cdot 3)\) and simplifies to \(i \cdot 15\).