Simplify the complex fraction (2 + 3i) / (3 - 2i).
Answer and explanation
Correct answer: C. i
- Step 1: Multiply by conjugate: (2 + 3i)(3 + 2i) / ((3 - 2i)(3 + 2i)). Step 2. Numerator = 6 + 4i + 9i + 6i^2 = 6 + 13i - 6 = 13i. Denominator = 3^2 + (-2)^2 = 13. Result = 13i / 13 = i. Answer: i. Why not the others: Multiplying by i rotates a complex number by 90 degrees: i*(3 - 2i) = 2 + 3i.
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