Which property of addition is shown below?
If x = a + bi and y = -a - bi, x + y = 0.

Solution:

The additive inverse identity of complex numbers says that there exists a unique complex number -z for z such that z + (-z) = 0.

In the above equation, the identity used is additive inverse.

Where x = a + bi is z and y = -a - bi is (-z)

then x + y = 0.

Example: Let z = -16 + 8i.

Then -z will be - (-16 + 8i)

⇒ -z = 16 - 8i

Thus, by using the additive identity z + (-z) = 0

⇒ -16 + 8i + 16 - 8i = 0

Which property of addition is shown below?
If x = a + bi and y = -a - bi, x + y = 0.

Summary:

The property of addition that satisfies the equation is additive inverse.