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# Arg

 Arg[z]gives the argument of the complex number z.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• 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 and .
• Arg[z] has a branch cut discontinuity in the complex z plane running from to 0.
• Arg automatically threads over lists.
The result is given in radians:
The result is given in radians:
 Out[1]=
 Out[2]=

 Out[1]=
 Scope   (4)
For purely real or imaginary arguments, exact results are returned:
For generic approximate complex arguments, approximate results are returned:
The precision of the output tracks the precision of the input:
Arg threads element-wise over lists and matrices:
Arg returns exact answers for exact numerical arguments:
Infinite arguments give symbolic results:
Arg threads element-wise over sparse arrays:
 Applications   (3)
Polar decomposition of a complex number:
Color a plot according to value of Arg:
Expand multivalued functions without making assumptions about variables:
Simplify expressions containing Arg:
Generate Arg from FullSimplify:
Use Arg as a target function in ComplexExpand:
Rescale Arg to run from 0 to 1:
Find the domain of positivity for a linear function:
Use Arg to specify assumptions about complex variables:
Degenerate cases give intervals as results :
Numerical decision procedures with default settings cannot simplify this expression:
The machine-precision result is incorrect:
The arbitrary-precision result indicates that the result may be incorrect:
Using a larger setting for \$MaxExtraPrecision gives the correct result:
The input contains a hidden zero, and simplifying the argument gets the correct answer:
The argument principle of complex analysis cannot be used because Arg has range :
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