Argument and Principal Value (arg(z) from tan⁻¹(y/x) with quadrant; Arg(z) in (−π, π])

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arg(z) from tan⁻¹(y/x) with quadrant; Arg(z) in (−π, π]

What each symbol means

SymbolWhat it stands for
zNon-zero z = x + iy
Arg(z)Principal argument in (−π, π]
arg(z)General argument = Arg(z) + 2kπ

When to use this

z ≠ 0. Use quadrant to fix θ; atan2(y,x) avoids x = 0 division issue.