Simplify the left-hand side (LHS) by multiplying the numerator and denominator by the conjugate of the denominator.

To solve the equation (2+j)/(1-j) = j(x+jy), we need to simplify both sides and then equate the real and imaginary parts. Step 1: Simplify the left-hand side (LHS) by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of 1-j is 1+j. (2+j)/(1-j) = (2+j)/(1-j) × (1+j)/(1+j) Step 2: Perform the multiplication in the numerator and denominator. Numerator: (2+j)(1+j) = 2(1) + 2(j) + j(1) + j(j) = 2 + 2j + j + j^2 Since j^2 = -1, this becomes 2 + 3j - 1 = 1 + 3j. Denominator: (1-j)(1+j) = 1^2 - j^2 = 1 - (-1) = 1 + 1 = 2. So, the LHS simplifies to: (1+3j)/(2) = (1)/(2) + (3)/(2)j Step 3: Simplify the right-hand side (RHS). j(x+jy) = jx + j^2y Since j^2 = -1, this becomes: jx - y = -y + jx Step 4: Equate the simplified LHS and RHS. (1)/(2) + (3)/(2)j = -y + jx Step 5: Equate the real parts and the imaginary parts of both sides. Equating the real parts: (1)/(2) = -y y = -(1)/(2) Equating the imaginary parts: (3)/(2) = x Thus, the values of x and y are: x = (3)/(2), y = -(1)/(2) x = (3)/(2), y = -(1)/(2) That's 2 down. 3 left today — send the next one.