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|^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 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .

For any two complex numbers z1 and z2 ,prove that |z1.z2|=|z1|.|z2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|