Which equation demonstrates the multiplicative identity property?
[tex]$(-3+5 i)+0=-3+5 i$[/tex]
[tex]$(-3+5 i)(1)=-3+5 i$[/tex]
[tex]$(-3+5 i)(-3+5 i)=-16-30 i$[/tex]
[tex]$(-3+5 i)(3-5 i)=16+30 i$[/tex]
Answer (2)
The equation that demonstrates the multiplicative identity property is ( − 3 + 5 i ) ( 1 ) = − 3 + 5 i . This property states that any number multiplied by 1 equals itself. Therefore, the correct answer is the second equation from the options given.
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The multiplicative identity property states that any number multiplied by 1 equals itself.
Examine each equation to determine which one demonstrates this property.
The equation ( − 3 + 5 i ) ( 1 ) = − 3 + 5 i demonstrates the multiplicative identity property.
Therefore, the answer is ( − 3 + 5 i ) ( 1 ) = − 3 + 5 i .
Explanation
Understanding the Multiplicative Identity Property The multiplicative identity property states that any number multiplied by 1 equals itself. We need to identify which of the given equations demonstrates this property.
Examining Each Equation Let's examine each equation:
( − 3 + 5 i ) + 0 = − 3 + 5 i : This equation demonstrates the additive identity property, where adding 0 to a number doesn't change the number.
( − 3 + 5 i ) ( 1 ) = − 3 + 5 i : This equation shows that multiplying the complex number ( − 3 + 5 i ) by 1 results in the same complex number. This demonstrates the multiplicative identity property.
( − 3 + 5 i ) ( − 3 + 5 i ) = − 16 − 30 i : This equation shows the multiplication of a complex number by itself, which is not related to the multiplicative identity property.
( − 3 + 5 i ) ( 3 − 5 i ) = 16 + 30 i : This equation shows the multiplication of a complex number by its conjugate, which is also not related to the multiplicative identity property.
Identifying the Correct Equation The equation that demonstrates the multiplicative identity property is ( − 3 + 5 i ) ( 1 ) = − 3 + 5 i .
Examples
The multiplicative identity property is a fundamental concept in mathematics. It's used in various applications, such as simplifying expressions, solving equations, and understanding the structure of number systems. For example, when you're working with algebraic expressions, you can use the multiplicative identity to rewrite terms without changing their value. This can be helpful in factoring, combining like terms, and performing other algebraic manipulations. Imagine you are baking a cake and the recipe calls for multiplying the amount of ingredients by 1 to serve the same amount of people. This is similar to the multiplicative identity property, where multiplying by 1 keeps the original value unchanged.
