Question:
Imaginary parts of \(\left(\frac{3 - 2i}{2i}\right)^2\) is equal to
Imaginary parts of \(\left(\frac{3 - 2i}{2i}\right)^2\) is equal to
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Always simplify complex fractions before squaring to avoid errors.
Updated On: Apr 25, 2026
- \(\frac{5}{4}\)
- \(\frac{-5}{4}\)
- 3
- -3
- \(\frac{3}{4}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Simplify inside first: \(\frac{3-2i}{2i} = \frac{3}{2i} - \frac{2i}{2i} = \frac{3}{2i} - 1\). Since \(\frac{1}{i} = -i\), \(\frac{3}{2i} = -\frac{3i}{2}\). So inside = \(-1 - \frac{3i}{2}\).
Step 2: Detailed Explanation:
Square: \((-1 - \frac{3i}{2})^2 = 1 + 3i + \frac{9i^2}{4} = 1 + 3i - \frac{9}{4} = -\frac{5}{4} + 3i\). Imaginary part = 3.
Step 3: Final Answer:
Option (C).
Simplify inside first: \(\frac{3-2i}{2i} = \frac{3}{2i} - \frac{2i}{2i} = \frac{3}{2i} - 1\). Since \(\frac{1}{i} = -i\), \(\frac{3}{2i} = -\frac{3i}{2}\). So inside = \(-1 - \frac{3i}{2}\).
Step 2: Detailed Explanation:
Square: \((-1 - \frac{3i}{2})^2 = 1 + 3i + \frac{9i^2}{4} = 1 + 3i - \frac{9}{4} = -\frac{5}{4} + 3i\). Imaginary part = 3.
Step 3: Final Answer:
Option (C).
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