Question

1. which equation demonstrates the commutative property of addition for complex numbers? (10 - 5i)+(5 - 10i)=(5 - 10i)+(10 - 5i) (0 - 5i)+(5 - i)+(5 + i)=(0 - 5i)+(5 - i)+(5 + i) (5+10i)+(- 5 - 10i)=0+0i (5 - 10i)(0 - 10i)+(5 + 0i)=(5 - 10i)(0 - 10i)+(5 - 10i)(5 + 0i)

Explanation:

Step1: Recall commutative property of addition

The commutative property of addition for complex numbers states that \(a + b=b + a\). We need to find an equation where the order of addition of complex - number terms is changed.

Step2: Analyze each option

• Option 1: \((10 - 5i)+(5 - 10i)=(5 - 10i)+(10 - 5i)\) shows the commutative property of addition for complex numbers. Here, \(a = 10 - 5i\) and \(b = 5 - 10i\), and the equation is in the form \(a + b=b + a\).
• Option 2: \([(10 - 5i)+(5 - i)]+(5 + i)=(10 - 5i)+[(5 - i)+(5 + i)]\) shows the associative property of addition for complex numbers (\((a + b)+c=a+(b + c)\)).
• Option 3: \((5 + 10i)+(-5 - 10i)=0+0i\) shows the additive - inverse property (\(a+(-a)=0\)).
• Option 4: The equation in option 4 is a more complex combination of operations and does not clearly represent the commutative property.

Answer:

\((10 - 5i)+(5 - 10i)=(5 - 10i)+(10 - 5i)\)