Problem 42917. Nth roots of unity

Created by Martin C.

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>First, find the n nth roots of unity. eg if n = 6, find the n distinct (complex) numbers such that n^6 = 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Root_of_unity\"><w:r><w:t>&lt;https://en.wikipedia.org/wiki/Root_of_unity</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Second, raise each root to the power pi (.^pi).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Third, sum the resulting numbers and use that as the output.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

137 Solutions
43 Solvers

Last Solution submitted on Oct 24, 2022

Last 200 Solutions

Problem Comments

Solution Comments

Solution 1497321

1 Comment

1 Comment

bainhome on 19 Apr 2018

Surely I shouldn't done this ugly string thing, that is bad for everyone. Without any doubt, Tim's solution is the best one

Solution 930578

1 Comment

1 Comment

Rafael S.T. Vieira on 30 Aug 2020

Nice trick.

Problem Recent Solvers43

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42917. Nth roots of unity

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers43

Suggested Problems

More from this Author3

Problem Tags

Community Treasure Hunt

Problem 42917. Nth roots of unity

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers43

Suggested Problems

More from this Author3

Problem Tags

Community Treasure Hunt

Players