For a complex number Z, if the argument of `(Z-a)(barZ-b)` is `(pi)/(4)` or `(-3pi)/(4)` (where a, b are two real numbers), then the value of ab such that the locus of Z represents a circle with centre `(3)/(2)+(i)/(2)` is (where, `i^(2)=-1`)

If arg ((z-(10+6i))/(z-(4+2i)))=(pi)/(4) (where z is a complex number), then the perimeter of the locus of z is

If arg ((z-(10+6t))/(z-(4+2i)))=(pi)/(5) (where z is a complex number), then the perimeter of the locus of z is

If (pi)/(3) and (pi)/(4) are argument of z_(1) and bar(z)_(2) then the value of arg (z_(1)z_(2)) is

If (pi)/(3) and (pi)/(4) are arguments of z_(1) and bar(z)_(2), then the value of arg (z_(1)z_(2)) is

If |2z-4-2i|=|z|sin((pi)/(4)-arg z) then the locus of z represents a conic where eccentricity e is

If the real part of (barz +2)/(barz-1) is 4, then show that the locus of the point representing z in the complex plane is a circle.

If the real part of (barz +2)/(barz-1) is 4, then show that the locus of the point representing z in the complex plane is a circle.

If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus of z is

If the argument of (z-a)(barz-b) is equal to that ((sqrt(3)+i)(1+sqrt(3)i)/(1+i)) where a,b,c are two real number and z is the complex conjugate o the complex number z find the locus of z in the rgand diagram. Find the value of a and b so that locus becomes a circle having its centre at 1/2(3+i)