Q. If `z=x+iy` satisfies the equation `arg(z-2) = arg(2z+3i)` then `3x-4y` is equal to:-
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The complex number z = x + i*y. It is given that arg(z - 2) = arg(2z + 3i).
arg(z - 2) = `tan^-1(y/(x-2))`
arg(2z + 3i) = `tan^-1((2y+3)/(2x))`
`tan^-1(y/(x-2))` = `tan^-1((2y+3)/(2x))`
=> `y/(x - 2) = (2y + 3)/(2x)`
=> 2xy = (2y+3)(x-2)
=> 2xy = 2xy+3x-4y-6
=> 3x - 4y = 6
The correct answer is option C.
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