Respuesta :
Equation B) (-3 + 5i) (1) = -3 + 5i demonstrates the multiplicative identity property
Further explanation
There are several number operations that involve multiplication:
- 1. commutative
[tex]\boxed{\bold{a\times b=b\times a}}[/tex]
- 2. associative
[tex]\boxed{\bold{a\times (b\times c)=(a\times b)\times c}}[/tex]
- 3. closed
Multiplication between integers will produce integers too
- 4. distributive property
* addition
[tex]\boxed{\bold{a\times(b+c)=a\times b+a\times c}}[/tex]
* substraction
[tex]\boxed{\bold{a\times(b-c)=a\times b-a\times c}}[/tex]
- 5. identity
The multiplicative identity property is a multiplicative property in mathematics where each number multiplied by 1 will produce the original number or can be stated simply :
"The product of any number and one is that number"
So The Multiplicative Identity is 1
can be stated in the formula:
[tex]\large{\boxed{\bold{a\times 1=1\times a=a}}}[/tex]
From the available answer choices
- a) (- 3 + 5i) + 0 = -3 + 5i
this is an addition operation and not multiplication while O is an identity in the sum operation, so the statement is false
- b) (-3 + 5i) (1) = -3 + 5i
this is a multiplication operation and 1 is a Multiplicative Identity of multiplication, so the statement is true
c) (-3 + 5i) (-3 + 5i) = -16-30i
d) (-3 + 5i) (-3 + 5i) = 16 + 30i
choice c and is a multiplication factor, so the statement is false
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Keywords: Multiplicative Identity property, integers, equation
The equation [tex]\boxed{a + b = a = b + a}[/tex] demonstrates the multiplicative identity.
Further explanation:
The equation that satisfies the condition of multiplicative identity for the complex number can be represented as,
[tex]a \times b = a = b \times a[/tex]
Here, [tex]a[/tex] is the multiplicative identity and it can be observed that the multiplicative identity would be 1 where [tex]b[/tex] is the complex number.
The equation that satisfies the condition of additive identity for the complex number can be represented as,
[tex]a + b = a = b + a[/tex]
Here, [tex]a[/tex] is the additive identity and it can be observed that the additive identity would be 0 where [tex]b[/tex] is the complex number.
Consider an example [tex]\left( { - 3 + 5i} \right) + 0 = - 3 + 5i[/tex].
It can be observed that the equation [tex]\left( { - 3 + 5i} \right) + 0 = - 3 + 5i[/tex] satisfies the condition of the additive identity as 0 is the additive identity.
Consider an example [tex]\left( { - 3 + 5i} \right)\left( 1 \right) = - 3 + 5i[/tex].
It can be observed that the equation [tex]\left( { - 3 + 5i} \right)\left( 1 \right) = - 3 + 5i[/tex] satisfies the condition of the multiplicative identity as 1 is the multiplicative identity.
Here, [tex]a{\text{ is }}\left( { - 3 + 5i} \right)[/tex] by comparing the general equation [tex]a \times b = a = b \times a[/tex]
Therefore, the second example [tex]\left( { - 3 + 5i} \right)\left( 1 \right) = - 3 + 5i[/tex] demonstrates the multiplicative identity.
Thus, in general the equation [tex]a + b = a = b + a[/tex] demonstrates the multiplicative identity.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Arithmetic properties
Keywords: Multiplication, multiplicative identity, equation, additive identity, condition, conjugate, arithmetic properties, sum, operation, real numbers.
