Problem with understanding Babinet's principle

[Coffee_]

I'm having some trouble with understanding Babinet's principle, which in a simple case should imply the following:

''If I send light through a single slit, then I observe a certain diffraction pattern at the screen. Now I replace the slit with a single obstruction of the same width as the slit, let's say a hair. Then, except for the central spot, the minima and maxima should be on exactly the same places as for the slit.''

This doesn't make sense to me at all. This would mean that BOTH patterns will have destructive points on the same place. The sum of the two patterns should result in the pattern that one would obtain without ANY obstruction at all. If I take the sum of the two forementioned patterns, I will still have destructive points since they were on the same place. However, an unobstructed wave should have no such destructive points.

 

[rude man]

The slit by itself produces a min-max pattern. Same with the hair. So you know the sum of the two must give you a totally even illumination pattern, as you say (superposition principle).

So, what is there that could cause this paradox? Hint: a monochromatic wave comprises amplitude and phase.