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Q.

Least positive argument of the 4^th root of the complex number $2 - i \sqrt{12}$ is

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a

$π / 6$

b

$5 π / 12$

c

$7 π / 12$

d

$11 π / 12$

answer is B.

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Detailed Solution

$\begin{array}{l} z^{4} = 2 (1 - \sqrt{3} i) = 4 (\frac{1}{2} - \frac{\sqrt{3}}{2} i) = 4 [\cos (- \frac{π}{3}) + isin (- \frac{π}{3})] \\ z = \sqrt{2} [\cos \frac{2 mπ - (π 3)}{4} + isin \frac{2 mπ - (π 3)}{4}]; \\ m = 1, z = \sqrt{2} [\cos (\frac{5 π}{12}) + isin (\frac{5 π}{12})] \end{array}$

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