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
You're on a roll — here's the solution for problem 6. Step 1: Write the given expression. We need to multiply the complex numbers (4-5i) and (3-2i). (4-5i)(3-2i) Step 2: Expand the product using the distributive property (FOIL method). Multiply each term in the first parenthesis by each term in the second parenthesis: 4(3) + 4(-2i) - 5i(3) - 5i(-2i) 12 - 8i - 15i + 10i^2 Step 3: Substitute i^2 = -1. 12 - 8i - 15i + 10(-1) 12 - 8i - 15i - 10 Step 4: Combine the real parts and the imaginary parts. Group the real terms and the imaginary terms: (12 - 10) + (-8i - 15i) 2 - 23i The expression in the form x+iy is 2-23i. The final answer is 2-23i. What's next?