Which equation demonstrates the additive identity property?
(7+4 i)+0=7+4 i
(7+4 i)(1)=7+4 i
(7+4 i)+(7-4 i)=14
(7+4 i)+(-7-4 i)=0
Answer (2)
The additive identity property states that adding 0 to any number does not change the number.
Examine each equation to determine if it fits the additive identity property.
The equation ( 7 + 4 i ) + 0 = 7 + 4 i demonstrates the additive identity property.
Therefore, the answer is ( 7 + 4 i ) + 0 = 7 + 4 i .
Explanation
Understanding the Additive Identity Property The additive identity property states that for any number a , a + 0 = a . We need to identify which of the given equations demonstrates this property.
Analyzing the Equations Let's examine each equation:
( 7 + 4 i ) + 0 = 7 + 4 i : This equation shows that adding 0 to the complex number 7 + 4 i results in the same complex number 7 + 4 i . This perfectly demonstrates the additive identity property.
( 7 + 4 i ) ( 1 ) = 7 + 4 i : This equation demonstrates the multiplicative identity property, where multiplying by 1 results in the same number.
( 7 + 4 i ) + ( 7 − 4 i ) = 14 : This equation shows the addition of two complex numbers, resulting in a real number. This demonstrates the concept of complex conjugates but not the additive identity property.
( 7 + 4 i ) + ( − 7 − 4 i ) = 0 : This equation shows the addition of a complex number and its additive inverse, resulting in 0. This demonstrates the additive inverse property, not the additive identity property.
Identifying the Correct Equation Based on the analysis, the equation that demonstrates the additive identity property is ( 7 + 4 i ) + 0 = 7 + 4 i .
Examples
The additive identity property is fundamental in various mathematical and real-world scenarios. For instance, when balancing a checkbook, adding zero to the balance doesn't change the amount of money you have. Similarly, in physics, if you have a system with a certain energy level and you add zero energy to it, the energy level remains the same. This principle ensures that certain operations do not alter the original state or value, maintaining consistency and predictability in calculations and processes.
The equation that demonstrates the additive identity property is ( 7 + 4 i ) + 0 = 7 + 4 i because it shows that adding zero does not change the value of the complex number. Other options illustrate different properties rather than the additive identity. Therefore, the correct choice is ( 7 + 4 i ) + 0 = 7 + 4 i .
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