Locus of the point u=cos(z) is illustrated with z on a conic centred origin. Move point F , point D , point E to alter the conic.[br]point I represents complex number u[br]point H represents complex number z[br]other variables are unnecessary, a trial in layer(1) with straight line instead of conic[br][br]some other loci are included

illustrate the property of the locus corresponding to different kinds of conic.