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Recently, we presented a general model for the light curves ofchromospherically active stars, where the observed light curve is interferenceof two real constant period light curves of long-lived starspots. In this firstpaper, we make six specific questions which undermine this argument, because itcontradicts the current widely held views about the stellar surfacedifferential rotation and the starspots. Our aim is to answer these sixquestions. We present evidence that the long-lived starspots of our generalmodel have already been detected in the earlier surface imaging studies. TheLomb-Scargle power spectrum method analysis of the real and the simulated dataof FK Com reveals that this method fails to detect the two real constant periodlight curves of our general model. If our model is valid, this method givesincompatible period, amplitude and minimum epoch estimates telling nothingabout the real periods, the real amplitudes and the real minimum epochs of thetwo real light curves. This would mean that all earlier one-dimensional periodanalyses of the light curves of chromospherically active stars have givenspurious results which have been widely and uncritically accepted since thediscovery of the starspots in the year 1947. However, we arrive at a dead end,because we can not solve the real light curves of FK Com. In our second paper,we solve these real light curves with a new two-dimensional period findingmethod, prove the validity of our general model, and answer all six questionsmade in this first paper.

Real light curves of FK Comae Berenices: Dead end