This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
❌ Incorrect. Your calculation for z is incorrect. Step 1: Identify the error in the student's work. The main error is in the first step of your solution. You incorrectly transformed the expression (5)/(2-i) - (3+2i) into 5 - (3+2i)(2-i). The term (5)/(2-i) must be simplified by multiplying the numerator and denominator by the conjugate of the denominator, not by moving the denominator to multiply the second term. Step 2: Correctly simplify the first term. (5)/(2-i) = (5)/(2-i) × (2+i)/(2+i) = (5(2+i))/(2^2 - i^2) = (10+5i)/(4 - (-1)) = (10+5i)/(5) = 2+i Step 3: Substitute the simplified term back into the expression for z. z = (2+i) - (3+2i) Step 4: Perform the subtraction. z = 2+i-3-2i z = (2-3) + (1-2)i z = -1-i The correct value for z in the form x+iy is -1-i. 3 done, 2 left today. You're making progress.