The correct option is [tex]\boxed{\bf option (a)}[/tex] i.e., [tex]\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}[/tex].
Further explanation:
Concept used:
The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.
[tex]\boxed{A+\left({B+C}\right)=\left({A+B}\right)+C}[/tex]
Here, in the above equation the value of [tex]A+\left({B+C}\right)[/tex] is always equal to the value of [tex]\left({A+B}\right)+C[/tex] whether the grouping of number is changes or not.
Calculation:
Now check the option to get the answer.
First check option (a)
[tex]\left({-4+i}\right)+4i=-4+\left({i+4i}\right)[/tex]
In the above equation the grouping of the number is changed.
Now check the values of left hand side and right hand side.
[tex]\begin{aligned}\left({-4+i}\right)+4i&=-4+\left({i+4i}\right)\\-4+5i&=-4+5i\end{gathered}[/tex]
The value of LHS is same as RHS.
Therefore, option (a) is correct.
Now check option (b)
[tex](-4+i)+4i=4i+(-4i+i)[/tex]
The term [tex]i[/tex] should be associated with [tex]4i[/tex] but it is associated with [tex]-4i[/tex].
Therefore the option (b) is incorrect.
Now check option (c)
[tex]4i\times (-4i+i)=(4i-4i)+(4i\times i)[/tex]
The above expression does not follow any property.
Therefore the option (c) is incorrect.
Now check option (d)
[tex](-4i+i)+0=-4i+i[/tex]
The above expression follows additive property not associative property.
Therefore the option (d) is incorrect.
Thus, the correct option is [tex]\boxed{\bf option (a)}[/tex] i.e., [tex]\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}[/tex].
Learn more:
1. A problem on simplification: https://brainly.com/question/573729
2. A problem on domain and range: https://brainly.com/question/3412497
Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Simplification
Keywords: Associative property, equation, property, addition, associative property of Addition, additive property, grouping terms, left hand side, right hand side, LHS, RHS.
