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

If |z_(1)|=|z_(2)|=....|z_(n)|=1 , then show that, |z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|

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

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

If z_(1)=4-3iand z_(2)=-12+5i, "show that", |z_(1)/z_(2)|=|z_(1)|/|z_(2)|

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)

Define addition and multiplication of two complex numbers z_1 and z_2 . Hence show that : R_e (z_1 z_2)=R_e (z_1)R_e (z_2)- I_m (z_1)I_m(z_2) .

If z_(1)=4-3iand z_(2)=-12+5i, "show that", |z_(1)z_(2)|=|z_(1)||z_(2)|