Discussion
Imaginary parts of \(\left(\frac{3 - 2i}{2i}\right)^{2}\) is equal to
Answer: C
The imaginary part is 3.
Simplify the fraction first by multiplying top and bottom by \(-i\):
\[ \begin{aligned} \frac{3 - 2i}{2i} &= \frac{(3 - 2i)(-i)}{2} = \frac{-2 - 3i}{2} \\ \left(\frac{-2 - 3i}{2}\right)^{2} &= \frac{4 + 12i + 9i^{2}}{4} \\ &= \frac{-5 + 12i}{4} = -\frac{5}{4} + 3i \end{aligned} \]
So the imaginary part is 3. \(-\frac{5}{4}\) is the real part, which is the trap; \(\frac{5}{4}\), \(-3\) and \(\frac{3}{4}\) come from sign or scaling slips.
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