Locate the complex numbers on a plane: `pi/6ltarg(z)ltpi/3`

Locate the complex number z such that log_((cos pi)/(6))[(|z-2|+5)/(4|z-2|-4)]<2

If the locus of the complex number z given by arg(z+i)-arg(z-i)=(2pi)/(3) is an arc of a circle, then the length of the arc is

Show that the complex number z, satisfying are (z-1)/(z+1)=(pi)/(4) lies on a circle.

Find the complex number z if arg (z+1)=(pi)/(6) and arg(z-1)=(2 pi)/(3)

If a point P denoting the complex number z moves on the complex plane such that,|Re(z)|+|Im(z)|=1 then locus of P is

If a point P denoting the complex number z moves on the complex plane such that |RE(z)|+|IM(z)|=1 then locus of P is

The point representing the complex number z for which arg (z-2)(z+2)=pi/3 lies on

If a point P denoting the complex number z moves on the complex plane such tha "Re"(z^(2))="Re"(z+bar(z)) , then the locus of P (z) is

(z|barz|^2)/(barz|z|^2) = _______ where z is a complex number of amplitude pi/3 .