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Why is the principal value of the argument of z always in the interval of -pi and pi?

Waterloo97
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1 Answers1

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It isn't. Sometimes the interval $[0,2\pi[$ is used. It is just convention.

Any half-open interval with length $2\pi$ would suffice, but $]-\pi,\pi]$ and $[0,2\pi[$ are the most popular one due to the intrinsic connections of argument to trigonometric functions.

Henricus V.
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