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Weird result in Mathematica 6

I was playing around with Mathematica 6 a bit and ran this command to
solve for the inverse of the Moebius transformation

 Reduce[(z - a)/(1 - a\[Conjugate] z) == w && a a\[Conjugate] < 1 &&
   w w\[Conjugate] < 1, z]]

This is what I got as a result:
-1 < w < 1 && -1 < a < 1 && z == (a + w)/(1 + w Conjugate[a])

Why is Mathematica assuming a and w are real? The Moebius
transformation is invertible in the unit disc regardless of whether a
and w are real or not. Any thoughts?

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