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http://functions.wolfram.com/01.04.16.0079.01
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Log[Subscript[z, 1]/Subscript[z, 2]] == Log[Subscript[z, 1]] -
Log[Subscript[z, 2]] + 2 I Pi /; Arg[Subscript[z, 1]] <= 0 &&
Arg[Subscript[z, 2]] >= Pi + Arg[Subscript[z, 1]]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", FractionBox[SubscriptBox["z", "1"], RowBox[List[" ", SubscriptBox["z", "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", SubscriptBox["z", "1"], "]"]], "-", RowBox[List["Log", "[", SubscriptBox["z", "2"], "]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Arg", "[", SubscriptBox["z", "1"], "]"]], "\[LessEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["z", "2"], "]"]], "\[GreaterEqual]", RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "1"], "]"]]]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mrow> <mtext> </mtext> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi>  </mi> <mo> ⁢ </mo> <mrow> <mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> ≥ </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mrow> <mtext> </mtext> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi>  </mi> <mo> ⁢ </mo> <mrow> <mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> ≥ </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", SubscriptBox["zz", "1"], "]"]], "-", RowBox[List["Log", "[", SubscriptBox["zz", "2"], "]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]], "\[LessEqual]", "0"]], "&&", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "2"], "]"]], "\[GreaterEqual]", RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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