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4-1.Complex numbers
medium
$(3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}$ નો કાલ્પનિક ભાગ ....... હોય શકે
A
$-2 \sqrt{6}$
B
$6$
C
$\sqrt{6}$
D
$-\sqrt{6}$
(JEE MAIN-2020)
Solution
$(3+2 \sqrt{-54})=3+2 \times 3 \times \sqrt{6} \mathrm{i}$
$=(3+\sqrt{6} \mathrm{i})^{2}$
$(3-2 \sqrt{54})=(3-\sqrt{6} \mathrm{i})^{2}$
$(3+2 \sqrt{-54})^{1 / 2}+(3-2 \sqrt{-54})^{1 / 2}$
$=\pm(3+\sqrt{6} \mathrm{i}) \pm(3-\sqrt{6} \mathrm{i})$
$=6,-6,2 \sqrt{6} \mathrm{i},-2 \sqrt{6} \mathrm{i}$
Standard 11
Mathematics
