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

Step-by-step solution

Given the determinant: vmatrix 2 & 3+i & -1 3-i & 0 & i-1 -1 & -1-i & 1 vmatrix = A + iB Expanding the determinant along the first row, we get: D = 2 vmatrix 0 & i-1 -1-i & 1 vmatrix - (3+i) vmatrix 3-i & i-1 -1 & 1 vmatrix - 1 vmatrix 3-i & 0 -1 & -1-i vmatrix Evaluating each 2 2 minor: First minor: vmatrix 0 & i-1 -1-i & 1 vmatrix = (0)(1) - (i-1)(-1-i) = 0 - (-(i^2 - 1)) = 0 - (-(-1 - 1)) = -2 Second minor: vmatrix 3-i & i-1 -1 & 1 vmatrix = (3-i)(1) - (i-1)(-1) = 3 - i + i - 1 = 2 Third minor: vmatrix 3-i & 0 -