The correct option is \(\boxed{\bf option (a)}\) i.e., \(\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}\).
Further explanation:
Concept used:
The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.
\(\boxed{A+\left({B+C}\right)=\left({A+B}\right)+C}\)
Here, in the above equation the value of \(A+\left({B+C}\right)\) is always equal to the value of \(\left({A+B}\right)+C\) whether the grouping of number is changes or not.
Calculation:
Now check the option to get the answer.
First check option (a)
\(\left({-4+i}\right)+4i=-4+\left({i+4i}\right)\)
In the above equation the grouping of the number is changed.
Now check the values of left hand side and right hand side.
\(\begin{aligned}\left({-4+i}\right)+4i&=-4+\left({i+4i}\right)\\-4+5i&=-4+5i\end{gathered}\)
The value of LHS is same as RHS.
Therefore, option (a) is correct.
Now check option (b)
\((-4+i)+4i=4i+(-4i+i)\)
The term \(i\) should be associated with \(4i\) but it is associated with \(-4i\).
Therefore the option (b) is incorrect.
Now check option (c)
\(4i\times (-4i+i)=(4i-4i)+(4i\times i)\)
The above expression does not follow any property.
Therefore the option (c) is incorrect.
Now check option (d)
\((-4i+i)+0=-4i+i\)
The above expression follows additive property not associative property.
Therefore the option (d) is incorrect.
Thus, the correct option is \(\boxed{\bf option (a)}\) i.e., \(\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}\).
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.
