" 9.यदि "|z-2|=2|z-1|," तो सिद्ध कीजिए कि "|z|^(2)=(4)/(3)Re(z)

If |z-2|=2|z-1| , then show that |z|^(2)=(4)/(3)Re(z) .

If |z-2|=2|z-1| , then show that |z|^(2)=(4)/(3)Re(z) .

If |Z-2|=2|Z-1| , then the value of (Re(Z))/(|Z|^(2)) is (where Z is a complex number and Re(Z) represents the real part of Z)

If |Z-2|=2|Z-1| , then the value of (Re(Z))/(|Z|^(2)) is (where Z is a complex number and Re(Z) represents the real part of Z)

If z_(1),z_(2) are complex number such that Re(z_(1) ) = |z_(1) - 1| , Re(z_(2)) = |z_(2) -1| and arg(z_(1) - z_(2)) = (pi)/(3) , then Im (z_(1) + z_(2)) is equal to

Given z is a complex number z^(2)-z-|z|^(2)+(64)/(|z|^(5))=0 and Re(z)!=(1)/(2) Then |z| is less than :

If z_(1) and z_(2) satisfy the equation |z-2|=|"Re"(z)| and arg (z1-z2)=pi/3, then Im (z1+z2) =k/sqrt 3 where k is

Locus of z in the following curves: Im(z)=|z-(1+2i)| and 4-Im(z)=|z-(1+2i)| represent A and B respectively. If locus of z in arg (z-(1+2i))=theta intersect A and B at points P(z_(1)) and Q(z_(2)) respectively, then minimum value of |z_(1)-(1+2i)||z_(2)-(1+2i)| is: (Re(z_(1))+Re(z_(2))!=2)

If |z_(1)|=1,|z_(2)|=2,|z_(3)|=3 ,then |z_(1)+z_(2)+z_(3)|^(2)+|-z_(1)+z_(2)+z_(3)|^(2)+|z_(1)-z_(2)+z_(3)|^(2)+|z_(1)+z_(2)-z_(3)|^(2) is equal to