If |2 3+i -1; 3-i 0 i-1; -1 -1-i 1| = A + iB, where i = √-1, then what is A + B equal to?

Expanding the determinant along row 1: 2·|0 i-1; -1-i 1| - (3+i)·|3-i i-1; -1 1| + (-1)·|3-i 0; -1 -1-i|. First minor: 0·1 - (i-1)(-1-i) = -(i-1)(-1-i) = (i-1)(1+i) = i + i² - 1 - i = -2. So 2·(-2) = -4. Second minor: (3-i)(1) - (i-1)(-1) = 3-i + i-1 = 2. So -(3+i)·2 = -6-2i. Third minor: (3-i)(-1-i) - 0 = -3-3i+i+i² = -4-2i. So -1·(-4-2i) = 4+2i. Total: -4 + (-6-2i) + (4+2i) = -6 + 0i. So A = -6, B = 0, A + B = -6.