       Re: Value of E

• To: mathgroup at smc.vnet.net
• Subject: [mg77386] Re: [mg77301] Value of E
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Thu, 7 Jun 2007 04:06:41 -0400 (EDT)
• Organization: Deep Space Corps of Engineers
• References: <30949593.1181133668382.JavaMail.root@m35>

```Both solutions depend on the ArcSin argument:

Off[Solve::"ifun"]
Solve[(I*a^(I*ArcSin[3/5]) - I*a^-(I*ArcSin[3/5]))/2 == 3/5, a]
N@%

{{a -> (-(4/5) - (3*I)/5)^(-(I/ArcSin[3/5]))}, {a -> (4/5 -  =

(3*I)/5)^(-(I/ArcSin[3/5]))}}
{{a -> 0.020608916569560962 + 0.*I}, {a -> 0.36787944117144233 + 0.*I}}

Solve[(I*a^(I*ArcSin[arg]) - I*a^-(I*ArcSin[arg]))/2 == arg, a]

{{a -> (-\[ImaginaryI] arg - Sqrt[1 - arg^2])^-\[ImaginaryI]/
ArcSin[arg]}, {a -> (-\[ImaginaryI] arg + Sqrt[
1 - arg^2])^-\[ImaginaryI]/ArcSin[arg]}}

Bobby

On Wed, 06 Jun 2007 06:22:44 -0500, Jeff Albert <albertj001 at hawaii.rr.co=
m>  =

wrote:

> Now we all know that:
>
> In:=N[E,10]
>> From In:=2.718281828459045
>
> and that
>
> In:=N[(I*E^(I*ArcSin[3/5])-I*E^-(I*ArcSin[3/5]))/2,10]
>> From In:=-0.6 + 0.*I.
>
>
> In:=NSolve[(I*A^(I*ArcSin[3/5])-I*A^-(I*ArcSin[3/5]))/2==3/=
5,A]
>> From In:=Solve::ifun: Inverse functions are being used by Solv=
e, so
> some solutions may not be found.
>> From In:={{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:=0.36787944117144233^(I*Pi)
>> From In:=-1. - 1.2246063538223773*^-16*I
>
> Jeff Albert
>
>
>
>

-- =

DrMajorBob at bigfoot.com

```

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