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Arg

Argument (complex analysis) (WMA link)

Arg[z, Method -> "option"]

returns the argument of a complex value z.

• Arg[z] is left unevaluated if z is not a numeric quantity.
  
• Arg[z] gives the phase angle of z in radians.
  
• The result from Arg[z] is always between -Pi and +Pi.
  
• Arg[z] has a branch cut discontinuity in the complex z plane running from -Infinity to 0.
  
• Arg[0] is 0.
  

• • Arg[-3]

Same as above, but using SymPy's method:

• • Arg[-3, Method->"sympy"]

• • Arg[1-I]

Arg evaluates the direction of DirectedInfinity quantities by the Arg of its arguments:

• • Arg[DirectedInfinity[1+I]]

• • Arg[DirectedInfinity[]]

Arg for 0 is assumed to be 0:

• • Arg[0]