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If the vertices of a triangle are $8 + 5 i, - 3 + i, - 2 - 3 i$ , the modulus and the argument of the complex number representing the centroid of this triangle respectively are:

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$2, \frac{π}{4}$

$\sqrt{2}, \frac{π}{4}$

$2 \sqrt{2}, \frac{π}{4}$

$2 \sqrt{2}, \frac{π}{2}$

answer is B.

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Detailed Solution

Centroid $= \frac{8 + 5 i - 3 + i - 2 - 3 i}{3}$

$p$ (say) $= 1 + i$

$| p | = \sqrt{1 + 1} = \sqrt{2}$

$\arg (p) = \tan^{- 1} (1 / 1) = π / 4$

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