If |z-1|=|z-5| and `Re(z)=k`; then evaluate k

If |z-1|=|z-5| and |z|=sqrt13 ,then find |Im(z)|

If |z-1| = |z-5| and |z|=sqrt(13) then find |Im(z)|

If |z|=k and omega=(z-k)/(z+k) , then Re (omega) =

If |z-3|=min{|z-1|,|z-5|} , then Re(z) equals to

If |z+1+3i|=1 ,then the least value of |z| is sqrt(k)+m ,then evaluate sqrt(k-m)

If |z-2-3i|=1 ,then the greatest value of |z| is sqrt(k)+m, then evaluate sqrt((k+m)+2)

If |z-3| = "min" {|z-1|,|z-5|} , then Re(z) equals to

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)|=2Re(z) then the locus of z is

Read the following writeup carefully: If z_1 = a+ib and z_2 =c + id be two complex numbers such that |z_1| = |z_2|=1 and "Re" (z_1 bar(z_2))=0 . Now answer the following question Let k = |z_1 + z_2| + |a+ ib| , then the value of k is