If z = x + iy, then | 3z - 1 | = 3 | z - 2 | represents
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|3(x+iy)-1|=3|(x+iy)-2|
|(3x-1 )+ i(3y)|=3|(x-2)+iy|
√[(3x-1)^2+(3y) ^2]=3√[(x-2)^2+y^2]
square both sides
(3x-1)^2+9y^2=9(x-2)^2 +9y^2
(3x-1)^2=9(x-2)^2
9x^2 +1 -6x=9x^2 +36 -36x
1-6x-36+36x=0
30x=35
x=7/6
this represents a straight line parallel to y axis
|(3x-1 )+ i(3y)|=3|(x-2)+iy|
√[(3x-1)^2+(3y) ^2]=3√[(x-2)^2+y^2]
square both sides
(3x-1)^2+9y^2=9(x-2)^2 +9y^2
(3x-1)^2=9(x-2)^2
9x^2 +1 -6x=9x^2 +36 -36x
1-6x-36+36x=0
30x=35
x=7/6
this represents a straight line parallel to y axis
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sorry I forgot there 9saqurey it's my mistake and ans is straight line that is x=-7/6 parallel to yaxis
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