Question

let z be a complex number satisfying |z-3|=|z-4i|, then find the least possible value of 10|z|.

Joshi sir comment

 

In |z-3|=|z-4i|, z represents all points lying on the perpendicular bisector of the line joining 3 and 4i in x-y plane. In this perpendicular bisector, if we draw a perpendicular then it will be the minimum magnitude of z. Construct this as a diagram we will get

sinθ = |z| / (7/8)

or |z| = (7/8)(4/5) = 7/10   

Read 1 Solution.

take z=x+iy and solve it acording to Iz-3I =I z-4i I

solving it you will get 6x-8y+7=0

now IzI = perpendicular distance of (0,0) from the line 6x-4y+7=0

solving it u  wll gt  IzI =7/10

therefore 10 IzI = 7

NIKHIL VARSHNEY 10 year ago is this solution helpfull: 3 0

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