JEE Main 2016 (30)

Algebra Level 5

The sum of the imaginary parts of all complex numbers , which simultaneously satisfy ∣ z − 12 z − 8 i ∣ = 5 3 , ∣ z − 4 z − 8 ∣ = 1 |\frac{z-12}{z-8i}|=\frac{5}{3},|\frac{z-4}{z-8}|=1 is: __________ \text{\_\_\_\_\_\_\_\_\_\_} .

Try my set JEE Main 2016 .
32 35 None of these 28 25

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Prakhar Bindal
Mar 23, 2016

The second equation is simply the equation of perpendicular bisector of the points (4,0) and (8,0) that is x=6 . so any point can be taken as (6,y). Substituted in equation 1 and see sum of roots (verify that quadratic has real roots) and we are done!

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