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Value of E


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




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