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

Answer 1

It'd be worthwhile to look up each of these 4 properties and then to determine which one applies to the given situation. I do see that "like terms" have been combined here; that is, we combine the real terms and then combine the imaginary terms, separately, resulting in the final a + bi.

Answer 2

The Identity property best suits your question. Identity property (or additive identity property) is used when zero can be added and still give you the same answer. However, like @mathmale said, it's best if you look them up too.

Answer 3

Good point, @msskyann. I missed that aspect of this problem.

@elocke: for discussions of identity property in mathematics, see the following:

https://www.google.com/search?espv=2&q=identity+math+problem&revid=2135615154&sa=X&ved=0ahUKEwjy9dLR_rbJAhUQRYgKHfNEACoQ1QIIbCgA&biw=1360&bih=673