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Re: How can I find roots in Mathematica 6?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg83558] Re: How can I find roots in Mathematica 6?
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Thu, 22 Nov 2007 06:40:12 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <fi3itn$afc$1@smc.vnet.net>
DrunkenButterfly wrote:
> Does anyone know what should I type in in order to find the roots of
>
> cosh(z)=i with Abs[Im[z]]<10 ?
>
> I've just started using Mathematica 6 and the help browser is not really helping me at all. Thanks!
Every built-in function name starts will an Uppercase letter (even if
the name is only one letter long) and square braces are used to pass
arguments (a function f(...) is written f[...], of course with some
meaningful arguments between the square braces). So cosh(z) is Cosh[z]
and the imaginary unit Sqrt[-1] is I (uppercase i). Test for equality is
denoted by == (a double equal sign, a single one is for assigning a
value to a symbol). Finally, the solver Reduce accepts a mix of
equalities and inequalities and works by default on the complex field.
Having said that,
In[1]:= Reduce[Cosh[z] == I && Abs[Im[z]] < 10, z]
Out[1]= z == -2*I*Pi - ArcCosh[I] || z == 2*I*Pi - ArcCosh[I] ||
z == -ArcCosh[I] || z == ArcCosh[I] ||
z == -2*I*Pi + ArcCosh[I] ||
z == 2*I*Pi + ArcCosh[I]
Regards,
--
Jean-Marc
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