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Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile Special thanks to these supporters: Jeff Straathof Christian Cooper Peggy Youell Ken Baron Today I Found Out Roman Urbanovski Mehdi Razavi John Buchan Bill Shillito Andrzej 'Yester' Fiedukowicz Susan Silver Lê OK Merli Spiked Math RexDex Thomas Buckingham Peter Kær Henry Reich George Greene Arnas Paul Bates Michael Surrago plusunim Tracy Parry Stan Ciprian Mark Klamerus Keith Vertrees Tyler O'Connor Kristian Joensen Valentin James P Buckley Michael