Final answer:
By expanding the product of the given complex numbers and equating real and imaginary parts, we find the solution (x, y) = (-5/13, 14/13), which corresponds to option B.
Step-by-step explanation:
To find the values of x and y in the complex number equation (x+iy)(2−3i)=4+i, we need to expand the product on the left side and then equate the real and imaginary parts with those on the right side.
Expanding the product, we have:
- (x × 2) + (x × -3i) + (iy × 2) + (iy × -3i) = 4 + i
- (2x - 3ix + 2iy - 3y) = 4 + i
Combining like terms, we get:
- Real part: 2x - 3y = 4
- Imaginary part: 2y - 3x = 1
Solving these two equations simultaneously for x and y, we find the solution that matches one of the given options.
Option B provides the solution: (x, y) = (-5/13, 14/13), which is the correct answer.