In the equation x + y = 0, where x and y are complex numbers (of the form a + bi), we see an illustration of the Inverse Property of Addition.
The Inverse Property of Addition states that for any real or complex number a, there exists an additive inverse -a such that:
a + (-a) = 0
Similarly, if we consider two complex numbers, x = a + bi and y = -a – bi, we find:
x + y = (a + bi) + (-a – bi) = (a – a) + (bi – bi) = 0 + 0i = 0
This shows that adding a complex number and its additive inverse will yield zero, indicating that y is indeed the additive inverse of x. Hence, the property in play here is the Inverse Property of Addition, which is a fundamental concept in both real and complex number arithmetic.
Understanding this property is crucial as it lays the groundwork for more advanced algebraic concepts and operations involving complex numbers.