Final answer:
By comparing the real and imaginary parts of the given complex numbers, the values for (a,b) that satisfy the equation are (-2, 2/3).
Therefore, the correct answer is: option B). (-2, 2/3)
Step-by-step explanation:
To find the values for (a,b) so that the equation (a+6) + (3b+1)i = 4+3i is true, we need to compare the real parts and the imaginary parts of the complex numbers on both sides of the equation.
For the real parts, we have a + 6 = 4.
Solving for a, we subtract 6 from both sides to get a = 4 - 6, which simplifies to a = -2.
For the imaginary parts, we have 3b + 1 = 3.
To find b, we subtract 1 from both sides to get 3b = 3 - 1, and then divide by 3 to obtain b = 2/3.
Therefore, the values for (a,b) that make the equation true are (-2, 2/3).