Re: Complex algebra problem

On 10 mayo, 14:56, "G. A. Edgar" <e...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article <1178820230.634330.188...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

<luir...@xxxxxxxxx> wrote:
What´s the solution of this equation?:
X = 2 ln(X).
Thanks. Ludovicus

No real solutions.
Complex solutions -2 W(-1/2), where W is the
Lambert W function. Get many
solutions by taking all the branches of W.

Using the principal branch of log, we get approximately
x = 1.588047265 + 1.540223501 i and
x = 1.588047265 - 1.540223501 i

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

Thanks Edgar
I would be able to find the solution applying the square root of a
complex number and then iterating:

sqr(x + yi) = .5*Log(x^2 + y^2) + i Arctg( y/x )

If z = 2*Log(z)

x + yi = Log(x^2 + y^2) + 2*Arctg(y/x)i

x^2 + y^2 = exp(x) ; tg ( y/2) = y/x

y = sqr(exp(x) - x^2)
x = y/tg(y/2)

Beginning with x=1 and iterating the two equations I obtained your
solution.
Ludovicus

.