If `w= z//[z-(1//3)i] and |w|=1`, then find the locus of z.

Let i= sqrt-1 . If a sequence of complex numbers is defined by z_(1)=0, z_(n+1)= z_(n)^(2)+i for n ge 1 , then find the value of z_(111) .

If z= (lamda + 3)- isqrt(5-lamda^(2)) , then the locus of z is a

If |z+bar(z)|= |z-bar(z)| , then the locus of z is

If z=sqrt3+i , find the conjugate of Z.

If z=x+iy is a complex number such that |z|=Re(iz)+1 , then the locus of z is

If |z|=1 and z ne +- 1 , then one of the possible values of arg(z)- arg (z+1)- arg (z-1) , is

If (w- bar(w)z)/(1-z) is purely real where w= alpha + ibeta, beta ne 0 and z ne 1 , then the set of the values of z is

Let w = (1 - iz)/( z -i). If |w| = 1, which of the following must be true?

If log_(sqrt3) ((|z|^(2)-|z|+1)/(2+|z|)) gt 2 , then the locus of z is

If z_(1) lies on the circle |z|=3 and x+iy =z_(1) + (1)/(z_(1)) then locus of z is