If `z_(1),z_(2) and z_(3)` are three distinct complex numbers such that `|z_(1)| = 1, |z_(2)| = 2, |z_(3)| = 4, arg(z_(2)) = arg(z_(1)) - pi, arg(z_(3)) = arg(z_(1)) + pi//2`, then `z_(2)z_(3)` is equal to

arg((z_(1))/(z_(2)))=arg(z_(1))-arg(z_(2))

arg(z_(1)z_(2))=arg(z_(1))+arg(z_(2))

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))

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 two non-zero complex numbers such tha |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg(z_(1))-arg(z_(2)) is equal to

|z_(1)|=|z_(2)| and arg((z_(1))/(z_(2)))=pi, then z_(1)+z_(2) is equal to

If z_(1),z_(2) are complex number such that Re(z_(1) ) = |z_(1) - 1| , Re(z_(2)) = |z_(2) -1| and arg(z_(1) - z_(2)) = (pi)/(3) , then Im (z_(1) + z_(2)) is equal to

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .

z_(1) "the"z_(2) "are two complex numbers such that" |z_(1)| = |z_(2)| . "and" arg (z_(1)) + arg (z_(2) = pi," then show that "z_(1) = - barz_(2).