To determine which equation demonstrates the multiplicative identity property, we need to recall what the multiplicative identity property states. The multiplicative identity property asserts that any number multiplied by 1 results in that same number. In mathematical terms, for any number [tex]\( a \)[/tex]:
[tex]\[ a \times 1 = a \][/tex]
Now, let's analyze each given option:
1. [tex]\((-3+5i) + 0 = -3+5i\)[/tex]
This equation shows the additive identity property, which states that adding 0 to any number leaves the number unchanged. So, this equation does not demonstrate the multiplicative identity property.
2. [tex]\((-3+5i)(1) = -3+5i\)[/tex]
Here, we multiply [tex]\((-3+5i)\)[/tex] by 1. According to the multiplicative identity property, multiplying any number by 1 should result in the number itself. Thus, this equation correctly demonstrates the multiplicative identity property, as [tex]\((-3+5i)(1)\)[/tex] indeed equals [tex]\((-3+5i)\)[/tex].
3. [tex]\((-3+5i)(-3+5i) = -16-30i\)[/tex]
This equation shows the product of [tex]\((-3+5i)\)[/tex] with another complex number [tex]\((-3+5i)\)[/tex]. This does not relate to the identity property as it involves squaring the complex number, which results in a completely different number.
4. [tex]\((-3+5i)(3-5i) = 16+30i\)[/tex]
This equation shows the product of [tex]\((-3+5i)\)[/tex] with [tex]\((3-5i)\)[/tex]. This also does not pertain to the identity property, as it involves multiplication by another complex number resulting in a different complex number.
By examining all the options, we can conclude that the second equation:
[tex]\[ (-3+5i)(1) = -3+5i \][/tex]
demonstrates the multiplicative identity property.
Therefore, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
