Number of `z,` which satisfy `Arg(z - 3 - 2i)=pi/6` and `Arg(z - 3 - 4i) = (2pi)/3` is/are :

if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

Let z be a complex number and i=sqrt(-1) then the number of common points which satisfy arg(z-1-i)=(pi)/(6) and arg((z-1-i)/(z+1-i))=(pi)/(2) is

The number of values of z satisfying both theequations Arg(z-1-i)=-(3 pi)/(4) and Arg(z-2-2i)=(pi)/(4) is

if arg(z+a)=(pi)/(6) and arg(z-a)=(2 pi)/(3) then

If arg(z - 1) = pi/6 and arg(z + 1) = 2 pi/3 , then prove that |z| = 1 .

Number of points of intersections of the curves Arg((z-1)/(z-3))=(pi)/(4) and Arg(z-2)=(3 pi)/(4) is/are

If arg(z+a) = pi//6 and arg(z-a) = 2 pi//3 (a in R^(+)) , then