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_2115.png?top_left_x=0&top_left_y=1204&width=532&height=275&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab320497","slug":"if-z-is-a-nonreal-root-of-sqrt7--1-then-zsup86sup-","content":"If z is a nonreal root of \\(\\sqrt[7]{- 1}\\) then z⁸⁶ + z¹⁷⁵ + z²⁸⁹ is equal to-","options":[{"_id":"68a399067f15af4716bb1a85","text":"0","sequence":0,"isCorrect":false},{"_id":"68a399067f15af4716bb1a86","text":"–1","sequence":1,"isCorrect":true},{"_id":"68a399067f15af4716bb1a87","text":"3","sequence":2,"isCorrect":false},{"_id":"68a399067f15af4716bb1a88","text":"1","sequence":3,"isCorrect":false}],"correct_answer":"–1","explanation":"**Sol**. z⁷ = –1,\n\n\\\\ expression = (z⁷)¹² . z² + (z⁷)²⁵ + (z⁷)⁴¹ . z²\n\n= (–1)¹² . z² + (–1)²⁵ + (–1)⁴¹ . z²\n\n= z² – 1 – z² = –1.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.628Z","__v":0,"vector_store_id":"5108e74d-e8b9-4ab7-8e56-cec20f6c9ea2","updated_at":"2024-08-30T21:49:39.628Z","isStarred":false},"params":{"questionSlug":"if-z-is-a-nonreal-root-of-sqrt7--1-then-zsup86sup-"}}]}]]

Question: If z is a nonreal root of \(\sqrt[7]{- 1}\) then z<sup>86</sup> + z<sup>175</sup> + z<sup>289</sup> ...

Solution