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How did complex numbers appear, what are they, and how did mathematicians come to the need to study them? What is the relationship between complex numbers and equations with all real roots? How are they represented geometrically and what operations can be performed with them? This is discussed by Alexey Savvateev, mathematician and mathematical economist, Doctor of Physical and Mathematical Sciences, Corresponding Member of the Russian Academy of Sciences, popularizer of mathematics among children and adults, scientific director of the Caucasian Mathematical Center of ASU, professor at the Moscow Institute of Physics and Technology, leading researcher at the Central Economics and Mathematics Institute of the Russian Academy of Sciences. Alexey Savvateev's channel "Matkult-privet!": / Matkultprivet Playlist "Alexey Savvateev": • Alexey Savvateev (Lectures) Playlist "Lectures on Mathematics": • Lectures on Mathematics #SciencePRO #Savvateev #AlexeySavvateev The video was created with the support of the Association of Volunteer Centers as part of the International Prize #MYVMESTE.