Скачать с ютуб How are they different? Cube root vs the exponent of 1/3 в хорошем качестве

How are they different? Cube root vs the exponent of 1/3

WolframAlpha gives different results if you try the cube root of -1 versus taking -1 to the exponent 1/3. Why is this happening? There is a good reason for the difference, which involves complex numbers and roots of equations. Special thanks this month to: Kyle, Lee Redden, Mike Robertson, Daniel Lewis. Thanks to all supporters on Patreon!   / mindyourdecisions   References https://www.wolframalpha.com/input?i=... https://www.wolframalpha.com/input?i=... https://www.wolframalpha.com/input?i=... https://en.wikipedia.org/wiki/Square_... https://en.wikipedia.org/wiki/Functio...) https://en.wikipedia.org/wiki/Princip... https://en.wikipedia.org/wiki/Princip... https://en.wikipedia.org/wiki/Nth_root https://math.stackexchange.com/questi... https://blog.wolframalpha.com/2013/04... Complex Variables and Applications, James Ward Brown, Ruel V. Churchill, 7th edition, Chapter 1 Section 8, Roots of Complex Numbers Subscribe: https://www.youtube.com/user/MindYour... Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. Book ratings are from January 2023. My Books (worldwide links) https://mindyourdecisions.com/blog/my... My Books (US links) Mind Your Decisions: Five Book Compilation https://amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.3/5 stars on 290 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews http://amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 https://amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews http://amzn.to/1NKbGlp 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter. My Blog https://mindyourdecisions.com/blog/ Twitter   / preshtalwalkar   Instagram   / preshtalwalkar   Merch https://teespring.com/stores/mind-you... Patreon   / mindyourdecisions   Press https://mindyourdecisions.com/blog/press