Which property of addition is shown below?If x = a + bi and y = -a – bi, x + y = 0.
The property of addition shown in the equation x + y = 0 is known as the additive inverse property
The property of addition shown in the equation x + y = 0 is known as the additive inverse property.
According to this property, the sum of any number and its additive inverse is always zero. In the given equation, x represents the complex number a + bi, and y represents the complex number -a – bi, where a and b are real numbers.
Therefore, when we add x and y, we get (a + bi) + (-a – bi), which simplifies to a – a + bi – bi. The real parts cancel each other out (a – a = 0), and the imaginary parts also cancel out (bi – bi = 0). Hence, the sum of x and y is indeed 0.
This property of addition is a fundamental concept in mathematics and plays a significant role in various mathematical operations and proofs.
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