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ArcSinh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Complex characteristics > Conjugate value





http://functions.wolfram.com/01.25.19.0007.01









  


  










Input Form





Conjugate[ArcSinh[x + I y]] == Log[Sqrt[(x + (4 x^2 y^2 + (1 + x^2 - y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 + x^2 - y^2, 2 x y]])^2 + (y + (4 x^2 y^2 + (1 + x^2 - y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 + x^2 - y^2, 2 x y]])^2]] - I ArcTan[x + (4 x^2 y^2 + (1 + x^2 - y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 + x^2 - y^2, 2 x y]], y + (4 x^2 y^2 + (1 + x^2 - y^2)^2)^(1/4) Sin[(1/2) ArcTan[1 + x^2 - y^2, 2 x y]]]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29