c is awkward; d won't work. "Imagine" is one of those verbs happier with a gerund (ing form) instead of an infinitive (to form).
English has the idiom "to labor under a delusion," which means to operate under a mental state of false ideas and of one's own making. An illusion is different, still false, but possibly created by another party like a hypnotist or magician. In both cases th