`If z,z_1 and z_2` are complex numbers, prove that(i) `arg(barz)= - argz` (ii)`arg(z_1 z_2) = arg(z_1) +arg(z_2)`

For any two complex numbers z1 and z2 ,prove that arg(z1.z2)=arg(z1)+arg(z2) .

If z_1 and z_2 are two non-zero complex numbers such that abs(z_1+z_2) = abs(z_1)+abs(z_2) , then arg(z_1)-arg(z_2) is equal to

Let z_(1)" and "z_(2) be complex numbers such that z_(1)+ i(bar(z_2))=0" and "arg(bar(z_1)z_2)=(pi)/(3) . Then arg(bar(z_1)) is

If z_(1) and z_(2) are to complex numbers such that two |z_(1)|=|z_(2)|+|z_(1)-z_(2)| , then arg (z_(1))-"arg"(z_(2))

If z_(1) and z_(2) are to complex numbers such that two |z_(1)|=|z_(2)|+|z_(1)-z_(2)| , then arg (z_(1))-"arg"(z_(2))

Statement-1 : let z_(1) and z_(2) be two complex numbers such that arg (z_(1)) = pi/3 and arg(z_(2)) = pi/6 " then arg " (z_(1) z_(2)) = pi/2 and Statement -2 : arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) + 2kpi, k in { 0,1,-1}

Statement-1 : let z_(1) and z_(2) be two complex numbers such that arg (z_(1)) = pi/3 and arg(z_(2)) = pi/6 " then arg " (z_(1) z_(2)) = pi/2 and Statement -2 : arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) + 2kpi, k in { 0,1,-1}

If z_(1) , z_(2) are complex numbers and if |z_(1) + z_(2)| = |z_(1)| - |z_(2)| show that arg (z_(1)) - arg (z_(2)) = pi .

If z_(1), and z_(2) are the two complex numbers such that|z_(1)|=|z_(2)|+|z_(1)-z_(2)| then find arg(z_(1))-arg(z_(2))