What property of addition is illustrated by the equation x + y = 0 when x = 1 + 2i and y = -1 – 2i?

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The equation you provided, x + y = 0, represents an interesting property of addition known as the Inverse Property of Addition.

In this specific situation, you have:

  • x = 1 + 2i
  • y = -1 – 2i

When you add these two complex numbers together:

x + y = (1 + 2i) + (-1 - 2i)

Here, we can combine like terms:

x + y = (1 - 1) + (2i - 2i)

This simplifies to:

x + y = 0 + 0i

Thus, we can see that:

x + y = 0

This demonstrates that the sum of a number and its additive inverse equals zero. In mathematical terms, y is the additive inverse of x. This property holds true for any pair of numbers, whether they are real, complex, or integers.

Therefore, the property illustrated in this case is indeed the Inverse Property of Addition, where each number can be paired with its negative to yield zero, emphasizing harmony and balance in arithmetic operations!

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