Re: Trigonometric form of complex numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg64224] Re: Trigonometric form of complex numbers
• From: Peter Pein <petsie at dordos.net>
• Date: Tue, 7 Feb 2006 03:35:50 -0500 (EST)
• References: <drus5c\$fok\$1@smc.vnet.net> <ds1s0r\$fni\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```ivan.svaljek at gmail.com schrieb:
> I'm looking for a solution that would produce something like this:
> r (cos f + i sin f).
>
> And would return n roots of a complex number in such form.
>
> Mathematica itself does nothing to return roots of complex numbers. Am
> I wrong ?
>
Sth. like
In[1]:= ComplexExpand[(-1)^(1/n)]
Out[1]= Cos[Pi/n] + I*Sin[Pi/n]

or

In[2]:= NSolve[x^5 == 1, x]
Out[2]= {{x -> -0.8090169943749475 - 0.5877852522924731*I},
{x -> -0.8090169943749475 + 0.5877852522924731*I},
{x -> 0.30901699437494745 - 0.9510565162951536*I},
{x -> 0.30901699437494745 + 0.9510565162951536*I}, {x -> 1.}}

??

```

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