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] `

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

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

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

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

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

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .

For all 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)) .

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)|

For any two complex numbers z_(1) and z_(2) prove that: |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|backslash z_(2)|^(2)+2Rebar(z)_(1)z_(2)