Question Detail

Expand: (3x + y + 7) + i(x - 2y) = 0 + 0i. So 3x + y + 7 = 0 and x - 2y = 0. From second, x = 2y. Substitute: 3(2y) + y + 7 = 0 => 6y + y + 7 = 0 => 7y = -7 => y = -1, then x = -2. So x = -2, y = -1. But options are given as pairs (x,y). Option B is (-1,3) which doesn't match. Option D is (4,-2). None match (-2,-1). Recheck: (3+i)x = 3x + ix, (1-2i)y = y - 2iy. Sum: (3x+y) + i(x-2y) + 7 = 0. So real: 3x+y+7=0, imag: x-2y=0 => x=2y. Then 3(2y)+y+7=0 => 7y=-7 => y=-1, x=-2. So x=-2, y=-1. Not in options. Possibly the equation was (3+i)x + (1-2i)y = 7i or something. Given the options, none match the correct solution.