JEE Mains · Maths · STD 11 - 4.1 complex nubers
The imaginary part of \((3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}\) can be
- A \(-2 \sqrt{6}\)
- B \(6\)
- C \(\sqrt{6}\)
- D \(-\sqrt{6}\)
Answer & Solution
Correct Answer
(A) \(-2 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
\((3+2 \sqrt{-54})=3+2 \times 3 \times \sqrt{6} \mathrm{i}\) \(=(3+\sqrt{6} \mathrm{i})^{2}\) \((3-2 \sqrt{54})=(3-\sqrt{6} \mathrm{i})^{2}\) \((3+2 \sqrt{-54})^{1 / 2}+(3-2 \sqrt{-54})^{1 / 2}\) \(=\pm(3+\sqrt{6} \mathrm{i}) \pm(3-\sqrt{6} \mathrm{i})\)…
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