To analyze the expression 3 + 4i + 5 + 6i + 3 + 5 + 4i + 6i, we need to identify which property of addition is being displayed. The property that applies here is the Commutative Property of Addition.
The Commutative Property states that the order in which two numbers are added does not affect the sum. In other words, a + b = b + a for any numbers a and b. In this expression, we can rearrange the terms in various ways, and the overall sum will remain the same.
Let’s break it down:
- The real parts are:
3 + 5 + 3 + 5. - The imaginary parts are:
4i + 6i + 4i + 6i.
No matter how we group or rearrange these components, the total for the real parts will equal 3 + 5 + 3 + 5 = 16, and the total for the imaginary parts will equal 4i + 6i + 4i + 6i = 20i.
By applying the commutative property, we can see that changing the order of the terms (e.g., 4i + 6i + 3 + 5 + 3 + 5 + 6i + 4i) will still yield the same final sum:16 + 20i.
This emphasizes the flexibility in how we can visualize and compute addition, ultimately confirming that the order of addition does not impact the result.