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
Step 1: Substitute x=i into the given function f(x). The function is f(x) = (x^5+2i)/(x^3). Substitute x=i: f(i) = (i^5+2i)/(i^3) Step 2: Evaluate the powers of i. Recall the properties of the imaginary unit i: i^1 = i i^2 = -1 i^3 = i^2 · i = -1 · i = -i i^4 = (i^2)^2 = (-1)^2 = 1 i^5 = i^4 · i = 1 · i = i Step 3: Substitute these values back into the expression for f(i). f(i) = (i+2i)/(-i) Step 4: Simplify the numerator. i+2i = 3i Step 5: Substitute the simplified numerator back into the expression. f(i) = (3i)/(-i) Step 6: Simplify the fraction. f(i) = -3 Step 7: Compare the result with the given options. A. i B. -4i C. -3 D. 2 The calculated value is -3, which corresponds to option C. The final answer is C. -3.