If the amplitude of ((z-2)/(z-6)) is (pi...

If the amplitude of `((z-2)/(z-6))` is `(pi)/(3)`, find its locus.

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If the amplitude of (z-1-2i) "is" pi/3 , then the locus of z is

`y=sqrt(3x)+(2-sqrt(3))`

`y=sqrt(3x)-sqrt3`

`x=sqrt(3y)+(2-sqrt3)`

`y= sqrt(3x)+2`

If the amplitude of z - 2 - 3i " is " pi//4 , then the locus of z = x +iy is

x+y - 1 = 0

x - y - 1= 0

x + y + 1 = 0

x - y +1 = 0

If z_(1) = 8 + 4i , z_(2) = 6 + 4i and z be a complex number such that Arg ((z - z_(1))/(z - z_(2))) = (pi)/(4) , then the locus of z is

`(x - 7)^(2) + (y- 5)^(2) = 2`

`(x - 7)^(2) + (y+ 5)^(2) = 2`

`(x - 7)^(2) + (y - 5)^(2) = 4`

`(x + 7)^(2) + (y + 5)^(2) = 4`