For any two complex numbers `z_1` and `z_2`, prove that `|z_1+z_2|<=|z_1|+|z_2|`, `|z_1-z_2|<=|z_1|+|z_2|`, `|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)| =|z_(1)|-|z_(2)| and |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 number z_(1) and z_(2) prove that: |z_(1)-z_(2)|<=|z_(1)|+|z_(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 z_(2) prove that: |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|backslash z_(2)|^(2)+2Rebar(z)_(1)z_(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)) .

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