For any two complex numbers ` z_1 and z_2 ` prove that: ` |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar 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)|

For any two complex number z_(1) and z_(2) prove that: |z_(1)-z_(2)|<=|z_(1)|+|z_(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 three complex numbers z_1, z_2 and z_3 , prove that z_1 lm (bar(z_2) z_3)+ z_2 lm (bar(z_3) z_1) + z_3lm(bar(z_1) z_2)=0 .

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)) .

Which of the following are correct for any two complex numbers z_1 and z_2? (A) |z_1z_2|=|z_1||z_2| (B) arg(|z_1 z_2|)=(argz_1)(arg,z_2) (C) |z_1+z_2|=|z_1|+|z_2| (D) |z_1-z_2|ge|z_1|-|z_2|

For any two complex numbers z_(1) and prove that quad Re(z_(1)z_(2))=Re z_(1)Re z_(2)-|mz_(1)|mz_(2)

For any two complex numbers z_(1),z_(2) the values of |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) , is