To determine the properties used when adding the given complex numbers [tex]\((4 + 3i) + (8 + 2i)\)[/tex], let’s analyze the steps involved in the calculation:
1. Start with the given expression:
[tex]\[
(4 + 3i) + (8 + 2i)
\][/tex]
2. Use the Associative Property of addition, which states that the way in which numbers are grouped in an addition operation does not change their sum. In this step, we group the real parts together and the imaginary parts together:
[tex]\[
(4 + 8) + (3i + 2i)
\][/tex]
3. Next, realize that rearranging the addends without changing their order uses the Commutative Property of addition, which states that the order in which two numbers are added does not change their sum. This is implicitly done during the re-grouping process:
[tex]\[
12 + 5i
\][/tex]
In summary, both the Associative Property and the Commutative Property are used in the process of adding these complex numbers.
Correct choices are:
A. Associative property
B. Commutative property
