Give an example of two complex numbers `z_(1) and z_(2)` such that `z_(1) ne z_(2) and |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 number z_(1) and z_(2) , such that |z_(1)| = |z_(2)| = 1 and z_(1) z_(2) ne -1 , then show that (z_(1) + z_(2))/(1 + z_(1)z_(2)) is real number.

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) =(|z_(1)|^(2)+|z_(2)|^(2))

If two complex numbers z_(1),z_(2) are such that |z_(1)|=|z_(2)| , is it then necessary that z_(1)=z_(2) ?