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A particle starts to travel from a point P on the curve $C_{1} : | z - 3 - 4 i | = 5$ , where |z| is maximum. From P, the particle moves through an angle tan^-1 $\frac{3}{4}$ in anticlock wise direction on |z- 3- 4i|= 5 and reaches at point Q. From Q, it comes down parallel to imaginary axis by 2 units and reaches at point R. Complex number corresponding to point R in the Argand plane is

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(3+5i)

(3+7i)

(3+8i)

(3+9i)

answer is B.

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Detailed Solution

$| z - 3 - 4 i | = 5 \Rightarrow (x - 3)^{2} + (y - 4)^{2} = 25$

$circle | z - 3 - 4 i | = 5 has centre at (3, 4)$

Point P is at a point with maximum value of $|z|$ . $∠ P O X = \tan^{- 1} (\frac{4}{3}) = 57 °$

Then it travels with an angle

$\tan^{- 1} 3 / 4 (37^{\circ}) in anti lockwise direction and It reaches Q (3, 9) above centre T hen it moves 2 units vertically downwards i.e. R (3, 7)$

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