Final answer:
The value of x+y is 13 - 13i and the value of xy is 69 - 109i.
Step-by-step explanation:
The question asks for the value of x+y and xy given that x = (10 − 3i) and y = (3 − 10i).
To find x+y, we add the real parts and the imaginary parts separately. So, x+y = (10 + 3) − (3 + 10)i = 13 - 13i. This means option A (13 - 13i) is correct.
To find xy, we use the distributive property. So, xy = (10 − 3i) * (3 − 10i) = 30 - 100i - 9i + 30i^2 = 30 - 109i - 30 = 69 - 109i. This means option C (69 - 149i) is correct.