Recently, we presented a general model for the light curves of chromospherically active stars, where the observed light curve is interference of two real constant period light curves of long-lived starspots. In this first paper, we make six specific questions which undermine this argument, because it contradicts the current widely held views about the stellar surface differential rotation and the starspots. Our aim is to answer these six questions. We present evidence that the long-lived starspots of our general model have already been detected in the earlier surface imaging studies. The Lomb-Scargle power spectrum method analysis of the real and the simulated data of FK Com reveals that this method fails to detect the two real constant period light curves of our general model. If our model is valid, this method gives incompatible period, amplitude and minimum epoch estimates telling nothing about the real periods, the real amplitudes and the real minimum epochs of the two real light curves. This would mean that all earlier one-dimensional period analyses of the light curves of chromospherically active stars have given spurious results which have been widely and uncritically accepted since the discovery 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 finding method, prove the validity of our general model, and answer all six questions made in this first paper.
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