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

The multiplicative identity property states that for any number \( a \), \( a \times 1 = a \). This means multiplying a number by 1 leaves it unchanged.

Step2: Analyze Each Option

• First option: \((-3 + 5i)+0=-3 + 5i\) uses the additive identity (adding 0), not multiplicative.
• Second option: \((-3 + 5i)(1)=-3 + 5i\) multiplies \(-3 + 5i\) by 1, which matches the multiplicative identity property.
• Third option: \((-3 + 5i)(-3 + 5i)=-16 - 30i\) is squaring the complex number, not using the identity.
• Fourth option: \((-3 + 5i)(3 - 5i)=16 + 30i\) is multiplying by a conjugate, not the identity element.

Answer:

\((-3 + 5i)(1) = -3 + 5i\) (the second option)