Question:
The imaginary part of
$(3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}$ can be :
Correct Option: 1
Solution:
$(3+2 \sqrt{-54})=3+2 \times 3 \times \sqrt{6} \mathrm{i}$
$=(3+\sqrt{6} i)^{2}$
$(3-2 \sqrt{54})=(3-\sqrt{6} i)^{2}$
$(3+2 \sqrt{-54})^{1 / 2}+(3-2 \sqrt{-54})^{1 / 2}$
$=\pm(3+\sqrt{6} \mathrm{i}) \pm(3-\sqrt{6} \mathrm{i})$
$=6,-6,2 \sqrt{6} i,-2 \sqrt{6} i$
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