test","extracted_subject":"MATH","extracted_chapter":"COMPLEX NUMBERS","extracted_topic":"INTEGRAL POWER OF IOTA, ALGEBRAIC OPERATIONS AND EQUALITY OF COMPLEX NUMBERS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2113.png?top_left_x=1064&top_left_y=849&width=532&height=217&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab32047f","slug":"if-a-is-a-complex-number-such-that-asup2sup-a-1-0-","content":"If a is a complex number such that a² + a + 1 = 0, then a³¹ is equal to","options":[{"_id":"68aa80877f15af4716d99645","text":"a","sequence":0,"isCorrect":true},{"_id":"68aa80877f15af4716d99646","text":"a²","sequence":1,"isCorrect":false},{"_id":"68aa80877f15af4716d99647","text":"0","sequence":2,"isCorrect":false},{"_id":"68aa80877f15af4716d99648","text":"1","sequence":3,"isCorrect":false}],"correct_answer":"a","explanation":"**Sol**. a = \\(\\frac{- 1 \\pm \\sqrt{1 - 4}}{2} = \\frac{- 1 \\pm \\sqrt{3}i}{2}\\)Ž a =\\(\\frac{- 1 + \\sqrt{3}i}{2}\\) = w\n\na³¹ = w³¹ = w = a Q a = \\(\\frac{- 1 - \\sqrt{3}i}{2}\\) = w²\n\na³¹ = (w²)³¹ = w⁶² = w² = a","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.626Z","__v":0,"vector_store_id":"d54ad80f-bcff-4741-8fbd-78f795841081","updated_at":"2024-08-30T21:49:39.626Z","isStarred":false},"params":{"questionSlug":"if-a-is-a-complex-number-such-that-asup2sup-a-1-0-"}}]}]]

Question: If a is a complex number such that a<sup>2</sup> + a + 1 = 0, then a<sup>31</sup> is equal to...

Solution