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Re: How can I find roots in Mathematica 6?

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  • Subject: [mg83558] Re: How can I find roots in Mathematica 6?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at>
  • Date: Thu, 22 Nov 2007 06:40:12 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fi3itn$afc$>

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]


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