Arg(z)-Arg(-z)=Arg(-1)=pi but Arg(-z)-Arg(z)=Arg(-1) is not equal to piexplain mathematically

We have Arg(Z) - Arg(-z) = Arg(-1) = pi . this information is given.

now we have to prove that Arg(-Z) - Arg(Z) = Arg(-1) ≠ pi.

from given information we can write as,

Arg(-Z) = Arg(Z) - pi.

plug this value in Arg(-Z) - Arg(Z) , we get,

Arg(Z) - pi - Arg(Z) = -pi .thsi proves the result.