Question

which equation demonstrates the additive identity property?

\\( (7+4i)+(7-4i)=14 \\)
\\( (7+4i)+0=7+4i \\)
\\( (7+4i)(1)=7+4i \\)
\\( (7+4i)+(-7-4i)=0 \\)

Explanation:

⚡ Using what you learned: Zero and Identity in Operations

Step 1: Identify the property

The additive identity property states that adding \(0\) to any number keeps its value identical:

$$ a + 0 = a $$

Step 2: Match with options

Evaluate the given choices:

• \((7+4i) + (7-4i) = 14\) (Additive inverse property of the imaginary parts)
• \((7+4i) + 0 = 7+4i\) (Adding \(0\) preserves the identity of the complex number)
• \((7+4i)(1) = 7+4i\) (Multiplicative identity property)
• \((7+4i) + (-7-4i) = 0\) (Additive inverse property)

The second equation demonstrates the additive identity property.

Answer:

\((7+4i) + 0 = 7+4i\)