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
Right Placide, let's go. To multiply and simplify (6 + 8i)(6 - 8i), we can use the difference of squares formula, which states that (a+b)(a-b) = a^2 - b^2. In the case of complex numbers, where i^2 = -1, the product of complex conjugates (a+bi)(a-bi) simplifies to a^2 + b^2. Step 1: Identify a and b from the expression. In (6 + 8i)(6 - 8i), we have a = 6 and b = 8. Step 2: Apply the formula for the product of complex conjugates. The formula is a^2 + b^2. Step 3: Substitute the values of a and b into the formula. 6^2 + 8^2 Step 4: Calculate the squares and sum them. 36 + 64 100 The simplified product is 100. Comparing this to the given options: A. 100 B. 80 C. 60 D. 40 The correct option is A. The final answer is A. 100. Send me the next one 📸