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If a complex number ‘z’ satisfies |2z + 10 + 10i| $\leq 5 \sqrt{3} - 5$ , then the least principal argument of ‘z’ is

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$- \frac{11 π}{12}$

$- \frac{π}{6}$

$- \frac{2 π}{3}$

$- \frac{5 π}{6}$

answer is A.

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Detailed Solution

$2 | z + 5 + 5 i \leq 5 (\sqrt{3} - 1) \Rightarrow | z + 5 + 5 i \leq \frac{5 (\sqrt{3} - 1)}{2}$

z lies interior region (or) on the boundary of the circle with centre at (–5, –5), radius $\frac{5 (\sqrt{3} - 1)}{2} .$
Least value of arg (z) is $\frac{- 5 π}{6}$

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