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

if z_(1)=2-i, and z_(2) = 1+ i, then find Im(1/(z_(1)z_(2)))

" 3.If "|z-1|=|z-5|" and "Re(z)=k;" then evaluate "k

if z_(1)=1-i and z_(2) = -2 + 4i then find Im((z_(1)z_(2))/barz_(1))

If |z_(1)| = sqrt(2), |z_(2)| = sqrt(3) and |z_(1) + z_(2)| = sqrt((5-2sqrt(3))) then arg ((z_(1))/(z_(2))) (not neccessarily principal)

Statement I: If |z_1+z_2|=|z_1|+|z_2|, then Im(z_1/z_2)=0 (z_1,z_2 !=0) Statement II: If |z_1+z_2|=|z_1|+|z_2| then origin, z_1, z_2 are collinear with 'z_1' and z_2 lies on the same side of the origin (z_1,z_2 !=0)

if |z-i Re(z)|=|z-Im(z)| where i=sqrt(-1) then z lies on

If z_(1)andz_(2) both satisfy z+ddot z=2|z-1| and arg(z_(1)-z_(2))=(pi)/(4), then find Im(z_(1)+z_(2))

If |z+4i|=min{|z+3i|,|z+5i|, then z satisfies Im z=-(7)/(2)