These words are derived from the same Latin term and share a meaning of "domineering," "overbearing," "dictatorial": "The judge had an imperious (or imperial) manner in court." Originally, imperious meant "befitting or suitable to an emperor or ruler," as in Shakespeare's lines from Hamlet: "Imperious Caesar, dead and turned to clay, / Might stop a hole to keep the wind away." Now, imperious is more often used to mean "imperative" or "urgent": "There is an imperious need for food in this stricken area." One might speak of an imperious dictator who lives in the imperial capital city of his country.
Dictionary of problem words and expressions. Harry Shaw. 1975.