To find the value of (z3 * z4) - (z2 * z1), we need to apply the complex number multiplication and subtraction rules. Let's calculate step by step:
z3 * z4 = (4 + 3i) * (-3 - 2i) = 4 * (-3) + 4 * (-2i) + 3i * (-3) + 3i * (-2i) = -12 - 8i - 9i + 6i^2 (where i^2 = -1) = -12 - 17i - 6 = -18 - 17i
z2 * z1 = (-1 - i) * (12 - i) = -1 * 12 - 1 * (-i) - i * 12 + i * (-i) = -12 + i - 12i - i^2 = -12 + i - 12i - (-1) = -12 + i - 12i + 1 = -11 - 11i
Now we can subtract: (z3 * z4) - (z2 * z1)
= (-18 - 17i) - (-11 - 11i) = -18 - 17i + 11 + 11i (applying subtraction rule) = -7 - 6i
Therefore, (z3 * z4) - (z2 * z1) equals -7 - 6i.
