Describing someone who has egomania, or showing the extreme self-obsession and belief in one's own superiority that comes with that condition.
From egomania plus the adjective-forming suffix -ical. This creates the adjectival form to describe people or behaviors characterized by egomania rather than the condition itself.
When you add -ical to egomania, you get a word that sounds almost as intense as it describes—egomaniacal rolls off the tongue like the obsession it names, with all those syllables stacking up.
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