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 12 year ago
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