Which property of addition is shown below if x a bi and y a bi x y 0?

The property of addition illustrated in the statement is the Additive Inverse Property.

In simple terms, the Additive Inverse Property states that for any number, there exists another number that, when added together, equals zero. In the case of your example, if we have complex numbers x = a + bi and y = – (a + bi), adding x and y gives us:

x + y = (a + bi) + (-(a + bi)) = a + bi - a - bi = 0

Therefore, when you add these two numbers together, the result is zero, clearly illustrating the Additive Inverse Property. This property is fundamental in mathematics, ensuring that every number has an opposite that allows for the cancellation out during addition.