{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42917,"title":"Nth roots of unity","description":"First, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Root_of_unity\u003e\r\n\r\nSecond, raise each root to the power pi (.^pi).\r\n\r\nThird, sum the resulting numbers and use that as the output. \r\n","description_html":"\u003cp\u003eFirst, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Root_of_unity\"\u003ehttps://en.wikipedia.org/wiki/Root_of_unity\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSecond, raise each root to the power pi (.^pi).\u003c/p\u003e\u003cp\u003eThird, sum the resulting numbers and use that as the output.\u003c/p\u003e","function_template":"function y = your_fcn_name(n)\r\n  y = 0;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct =  -0.467800202134647;\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 50;\r\ny_correct = -2.151544927902936 - 0.430301217000093i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 7;\r\ny_correct =   -0.435928596902380\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n\r\n%%\r\nn = 70;\r\ny_correct =   -3.031653804728051 - 0.430301217000095i\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":65480,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-08-01T00:25:42.000Z","updated_at":"2026-02-24T14:03:00.000Z","published_at":"2016-08-01T00:25:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst, find the n nth roots of unity. eg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Root_of_unity\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Root_of_unity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond, raise each root to the power pi (.^pi).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird, sum the resulting numbers and use that as the output.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":42917,"title":"Nth roots of unity","description":"First, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Root_of_unity\u003e\r\n\r\nSecond, raise each root to the power pi (.^pi).\r\n\r\nThird, sum the resulting numbers and use that as the output. \r\n","description_html":"\u003cp\u003eFirst, find the n nth roots of unity.\r\neg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Root_of_unity\"\u003ehttps://en.wikipedia.org/wiki/Root_of_unity\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSecond, raise each root to the power pi (.^pi).\u003c/p\u003e\u003cp\u003eThird, sum the resulting numbers and use that as the output.\u003c/p\u003e","function_template":"function y = your_fcn_name(n)\r\n  y = 0;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct =  -0.467800202134647;\r\nassert( abs(your_fcn_name(n)-y_correct) \u003c .0001)\r\n\r\n%%\r\nn = 50;\r\ny_correct = -2.151544927902936 - 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