Re: Writing a real valued expression in a form that does not include sqrt(-1)

On Sun, 11 May 2008, Szabolcs wrote:
On May 11, 7:41 pm, "G. A. Edgar" <ed...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
Szabolcs <szhor...@xxxxxxxxx> wrote:

I was wondering if the following real-valued expression (obtained
with a CAS) could be written in a form that does not include the
imaginary unit (denoted by i here). I would like to do this without
using trigonometric functions (actually this expression is equal to
cos(pi/ 9))

(1/2)*((1 + i*sqrt(3))/2)^(1/3) + (4*(1 + i*sqrt(3)))^(-1/3)

Is this possible?
casus irreducibilis

Ah, thanks for the pointer. This is what happens when one just
blindly relies on CASs instead of learning something about 3rd order
equations.

Computers promulgate artificial stupidly.

The equation was:

-(1/2) - 3*x + 4*x^3 == 0

Of course it has one real root.
Likely your favorite cos pi/9.
.

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