Question

which equation demonstrates the multiplicative identity property?
○ $(-3 + 5i) + 0 = -3 + 5i$
○ $(-3 + 5i)(1) = -3 + 5i$
○ $(-3 + 5i)(-3 + 5i) = -16 - 30i$
○ $(-3 + 5i)(3 - 5i) = 16 + 30i$

Explanation:

Step1: Recall multiplicative identity rule

The multiplicative identity property states that for any number \(a\), \(a \times 1 = a\).

Step2: Match to given options

Check each option against the rule:

• Option1: \((-3+5i)+0=-3+5i\) uses additive identity (0), not multiplicative.
• Option2: \((-3+5i)(1)=-3+5i\) follows \(a \times 1 = a\).
• Option3: \((-3+5i)(-3+5i)=-16-30i\) is squaring a complex number, not identity.
• Option4: \((-3+5i)(3-5i)=16+30i\) is multiplying by a conjugate, not identity.

Answer:

B. \((-3+5i)(1)=-3+5i\)