The sum of the real parts of the complex numbers satisfying the equations |z−4iz−2i|=1 and |z−8+3iz+3i|=35 is k5, then ‘k’ satisfies

4 ≤ k ≤ 25 , 2 ≤ k < 28 , 4 ≤ k ≤ 28

The sum of the real parts of the complex numbers satisfying the equations |z−4iz−2i|=1 and |z−8+3iz+3i|=35 is k5, then ‘k’ satisfies

| z − 4 i z − 2 i | = 1 ⇒ z = x + 3 i u sin g t h i s i n | z − 8 + 3 i z + 3 i | = 3 5 ⇒ 5 | x − 8 + 6 i | = 3 | x + 6 i | ⇒ x = 8 , 17 t w o c o m p l e x n u m b e r s 8 + 3 i , 17 + 3 i s u m o f r e a l p a r t = 8 + 17 = 25

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The sum of the real parts of the complex numbers satisfying the equations $| \frac{z - 4 i}{z - 2 i} | = 1$ and $| \frac{z - 8 + 3 i}{z + 3 i} | = \frac{3}{5} i s \frac{k}{5},$ then ‘k’ satisfies

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$2 \leq k < 25$

$4 \leq k \leq 25$

$2 \leq k < 28$

$4 \leq k \leq 28$

answer is B, C, D.

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Detailed Solution

$| \frac{z - 4 i}{z - 2 i} | = 1 \Rightarrow z = x + 3 i u \sin g t h i s i n | \frac{z - 8 + 3 i}{z + 3 i} | = \frac{3}{5} \Rightarrow 5 | x - 8 + 6 i | = 3 | x + 6 i | \Rightarrow x = 8, 17$