What is the definition of argument?

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Q What is the definition arg(f(s)), where s is a complex variable?

A If f is a rational function of complex variables, it is always possible to rewrite it in terms of its modulus and argument. In particular, you will always be able to find Re(f(s)) and Im(f (s)). From there, the modulus is defined as \(M(f(s))=\sqrt{(Re(f(s))^2+Im(f(s))^2)}\), while the argument or phase is defined as the \(atan(\frac{Im(f(s))}{Re(f(s))})\) .

--Elisa