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 are correct that we can calculate the product of the modulus of z and z itself. However, the image for question 85 explicitly asks for z^5. Let's calculate the product of the modulus of z and z itself, as you requested. Step 1: Find the modulus of z. Given z = sqrt(3) + i. The modulus r is: r = |z| = sqrt((3))^2 + (1)^2 = sqrt(3 + 1) = sqrt(4) = 2 Step 2: Calculate the product of |z| and z. |z| · z = 2 · (sqrt(3) + i) |z| · z = 2sqrt(3) + 2i This result, 2sqrt(3) + 2i, does not match any of the options provided for question 85 in the image (A. 2, B. 3+i, C. 3-i, D. 4). As previously calculated, if the question is indeed asking for z^5: z^5 = -16sqrt(3) + 16i This also does not match any of the given options. The final answer for the product of the modulus of z and z itself is 2sqrt(3) + 2i.