If `z=z_(1) z_(2) z_(3)….....z_(n)` prove that `"arg" z- ("arg" z_1 + "arg" z_2 + ….........+ "arg" z_(n) )=2n pi_(1) n in I`.

If | z_ (1) + z_ (2) | = | z_ (1) -z_ (2) |, then arg z_ (1) -arg z_ (2) =

If |z_1| = |z_2| and "arg" (z_1) + "arg" (z_2) = pi//2, , then

If z_(1),z_(2).........z_(n)=z, then arg z_(1)+arg z_(2)+......+argz_(n) and arg z differ by a

If arg (bar (z) _ (1)) = arg (z_ (2)) then

If |z_(1)+z_(2)|>|z_(1)-z_(2) then prove that -(pi)/(2)

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)

If z_(1),z_(2),z_(3) are three complex numbers and A=|{:("arg z"_(1),"arg z"_(2),"arg z"_(3)),("arg z"_(2),"arg z"_(3),"arg z"_(1)),("arg z"_(3),"arg z"_(1),"arg z"_(2)):}| then A is divisible by

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

Let | z_ (1) | = | z_ (2) | and arg (z_ (1)) + arg (z_ (2)) = (pi) / (2) then