       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:= Reduce[Cosh[z] == I && Abs[Im[z]] < 10, z]

Out= 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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