Prove the identity,`|1-z_1barz_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2)`

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|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 be two complex numbers prove that |z_1+z_2|^2+|z_1-z_2|^2=2[|z_1|^2+|z_2|^2]

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2 +|\z_1-z_2|^2=2[|\z_1|^2+|\z_2|^2]

if for the complex numbers z_1 and z_2 abs(1-barz_1z_2)^2-abs(z_1-z_2)^2 = k(1-abs(z_1)^2)(1-abs(z_2)^2) , then k is equal to

z_1 and z_2 be two complex no. then prove that abs(z_1+z_2)^2+abs(z_1-z_2)^2=2[abs(z_1)^2+abs(z_2)^2]

Prove that |(z_1- z_2)/(1-barz_1z_2)|lt1 if |z_1|lt1,|z_2|lt1

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_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 and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot