Value of E

*To*: mathgroup at smc.vnet.net*Subject*: [mg77301] Value of E*From*: "Jeff Albert" <albertj001 at hawaii.rr.com>*Date*: Wed, 6 Jun 2007 07:22:44 -0400 (EDT)

Now we all know that: In[112]:=N[E,10] >From In[112]:=2.718281828459045 and that In[113]:=N[(I*E^(I*ArcSin[3/5])-I*E^-(I*ArcSin[3/5]))/2,10] >From In[113]:=-0.6 + 0.*I. Can someone please explain: In[117]:=NSolve[(I*A^(I*ArcSin[3/5])-I*A^-(I*ArcSin[3/5]))/2==3/5,A] >From In[117]:=Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found. >From In[117]:={{A -> 0.020608916569560966 + 0.*I}, {A -> 0.36787944117144233 + 0.*I}} Where it turns out that the first solution seems to depend on the argument for ArcSin[], but the second does not. Indeed one even finds: In[115]:=0.36787944117144233^(I*Pi) >From In[115]:=-1. - 1.2246063538223773*^-16*I Jeff Albert

**Follow-Ups**:**Re: Value of E***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>