High Quality Content by WIKIPEDIA articles! In considering complex multiple-valued functions in complex analysis, the principal values of a function are the values along one chosen branch of that function, so it is single-valued. Complex valued elementary functions can be multiple valued over some domains. Determining the principal value of some of these functions can be obtained by decomposing the function into simpler ones whereby the principal value of the simple functions are straightforward to obtain. Now, arg z is intrinsically multivalued. One often defines the argument of some complex number to be between - (exclusive) and (inclusive), so we take this to be the principal value of the argument, and we write the argument function on this branch Arg z (with the leading capital A).

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