If `z` satisfies `|z-1|<|z+3|` then `omega=2z+3-i,` (where `i=sqrt-1`) sqtisfies

If z_(1) satisfies |z-1|=1 and z_(2) satisfies |z-4i|=1 , then |z_(1)-z_(2)|_("max")-|z_(1)-z_(2)|_("min") is equal to ___________

If z satisfies |z-2+2i|<=1 then

If z satisfies z-(1)/(z)=2i sin5^(@) and z^(6)+(1)/(z^(6))=2i sin theta then [|cot theta|] is equal to (where I.] denotes the greater integer function)

If z satisfies abs(z-1)+abs(z+1)=2 , then locus of z is

If z =x +iy satisfies |z+1-i|=|z-1+i| then

If a complex number z satisfies |z| = 1 and arg(z-1) = (2pi)/(3) , then ( omega is complex imaginary number)

If a complex number z satisfies |z|^(2)+1=|z^(2)-1| , then the locus of z is

The real part of the complex number z satisfying |z-1-2i|le1 and having the least positive argument, is