Question

which property of addition is shown in the equation below?

\\(a + bi + 0 + 0i = a + bi\\)

• commutative property
• inverse property
• identity property
• associative property

Explanation:

Identify the given equation

$$ (a + bi) + (0 + 0i) = a + bi $$

Analyze the operation

$$ z + 0 = z \quad \text{where} \quad z = a + bi \quad \text{and} \quad 0 = 0 + 0i $$

Determine the property

$$ \text{Adding the complex zero element } 0 + 0i \text{ to any complex number } a + bi \text{ leaves it unchanged, demonstrating the identity property of addition.} $$

Answer:

• commutative property
• inverse property
• identity property (Correct answer)
• associative property