Final answer:
The property of addition shown by the equation where x=bi and y=-a-bi, resulting in x+y=0, is the Additive Inverse Property.
Step-by-step explanation:
The property of addition that is shown by the equation x+y=0 where x=bi and y=-a-bi, is the Additive Inverse Property. This property states that for every number x, there exists a number y, which is the inverse of x, such that when they are added together, the result is zero. In this case, bi and -a-bi are inverses of each other because when added, the imaginary parts (bi and -bi) cancel each other out, and the real part -a cancels with an implicit +a (if any existed), resulting in zero.