If z_1and z_2 are any two complex numbers show that `|z_1+z_2|^2+|z_1-z_2|^2=2|z_1|^2+2|z_2|^2`

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

If z_(-)1 and z_(-)2 are any two complex numbers show that |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2|z_(1)|^(2)+2|z_(2)|^(2)

If z_(1) and z_(2), are two complex numbers such that |z_(1)|=|z_(2)|+|z_(1)-z_(2)|,|z_(1)|>|z_(2)|, then

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)|+|z_(1)-z_(2)| then

If z_(1) and z_(2) are two complex numbers such that z_(1)+2,1-z_(2),1-z, then

Statement-1 If|z_1| and |z_2| are two complex numbers such that |z_1|=|z_2|+|z_1-z_2|, then Im(z_1/z_2)=0 and Statement-2: arg(z)=0 =>z is purely real

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1, then

If z_1 and z_2 are two complex numbers, then prove that |z_1 - z_2|^2 le (1+ k)|z_1|^2 +(1+K^(-1) ) |z_2|^2 AA k in R^(+) .