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FullSimplify[ArcCos[x]+I ArcCosh[x]]

Alex Papkov
Posted 9 years ago

Hi! My Mathematica does not understand that

FullSimplify[ArcCos[x]+I ArcCosh[x]]

is zero. How can I make simplifications like this? Or it is just I am using older version, isn't it, and a new version already works with such expressions, does it? Best, Alex
POSTED BY: Alex Papkov
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Alex Papkov
Alex Papkov
Posted 9 years ago

Thank you, I understand now. -1<x<1 helped for my problem. Thanks again!
POSTED BY: Alex Papkov

Only works in range -Infinity < x < 1

FullSimplify[ArcCos[x] + I ArcCosh[x], Assumptions -> -Infinity < x < 1]
(*  0  *)
Plot[ArcCos[x] + I ArcCosh[x], {x, -2, 2}, PlotRange -> {{-2, 2}, {-1, 1}}, 
PlotStyle -> {Black, Thickness[0.02]}]

enter image description here

  NumberLinePlot[{-Infinity < x < 1}, {x, -2, 2}, PlotTheme -> "Detailed"]

enter image description here
POSTED BY: Mariusz Iwaniuk

Because in general it is not:

ArcCos[x] + I ArcCosh[x]
% /. x -> -1.0 - 1.0 I

gives:

4.47407 + 2.12255 I
POSTED BY: Sander Huisman
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