If `z_1a n dz_2` are two complex numbers and `c >0` , then prove that `|z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot`

If z_(1) and z_(2) are two complex numbers and c>0, then prove that |z_(1)+z_(2)|^(2)<=(1+c)|z_(1)|^(2)+(1+c^(-1))|z_(2)|^(2)

If z_(1) and z_(2) are two complex numbers and c>0 then prove that (z_(1)+z_(2))^(2)<=(1+c)|z_(1)|^(2)+(1+c^(-1))|z_(2)|^(2)

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^(+) .

If z_(1) and z_(2) are two complex numbers then prove that |z_(1)-z_(2)|^(2)<=(1+k)z_(1)^(2)+(1+(1)/(k))z_(2)^(2)

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|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

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

If z_(1) and z_(2)(ne0) are two complex numbers, prove that: (i) |z_(1)z_(2)|=|z_(1)||z_(2)| (ii) |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|),z_(2)ne0 .

For any two complex number z_(1) and z_(2) prove that: |z_(1)+z_(2)|>=|z_(1)|-|z_(2)|