Question

which property of multiplication is shown below?

if \\(x = a + bi\\) and \\(y = c + di\\), \\(x \times y = y \times x\\).

• commutative property
• identity property
• distributive property
• associative property

Explanation:

⚡ Using what you learned: Introduction to Complex Numbers · 🆕 New: Properties of Real and Complex Numbers
Order doesn't matter when multiplying.

Step 1: Analyze the given statement

The statement is:
If \( x = a + bi \) and \( y = c + di \), then:

$$ x \times y = y \times x $$

This shows that when we multiply two complex numbers \( x \) and \( y \), the order in which we multiply them does not change the result.

Step 2: Identify the algebraic property

• Commutative Property: States that changing the order of the operands does not change the result. For multiplication, \( A \times B = B \times A \).
• Identity Property: States that multiplying a number by \( 1 \) leaves it unchanged (\( A \times 1 = A \)).
• Distributive Property: Relates multiplication and addition, stating that \( A \times (B + C) = A \times B + A \times C \).
• Associative Property: States that when multiplying three or more numbers, the grouping does not affect the product (\( (A \times B) \times C = A \times (B \times C) \)).

Since the equation shows \( x \times y = y \times x \), it is demonstrating the commutative property of multiplication.

Answer:

commutative property