tinny math question!!!

Yes , Arg differs from arg .
For any complex number z=a+bi (where a and b are real) ,arg(z) represents the angle θ turned from the positive real axis of z .
However , the argument θ (or arg(z)) has infinitely many values ,so , Arg(z) is defined as the argument θ (or arg(z)) lying in the range -π≤θ≤π ,that is the principal value of argument .
For example ,If θ=π/4 ,we can say arg(z) equals π/4 ,2π+(π/4) ,4π+(π/4) ,........But if the θ is restricted to its principal value ,that Arg(z) can only equal π/4.