How did imaginary numbers come into existence? What was the first problem that required use of imaginary number?
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This is a fascinating subject, and it involves a story of intrigue, duplicity, death and betrayal in medieval Europe. Imaginary numbers appeared in efforts to solve cubic equations hundreds of years ago (equations with cubic terms like x^3). Nearly all mathematicians who encountered problems that seemed to require using imaginary numbers dismissed those solutions as nonsensical. A literal handful however, followed the math to where it led, and developed solutions that required the use of imaginary numbers. Over time, mathematicians and physicists discovered (uncovered?) more and more real world applications where the use of imaginary numbers was the best (and often only) way to complete complex calculations. The universe seems to incorporate imaginary numbers into its operations. This (https://www.youtube.com/watch?v=cUzklzVXJwo) does an excellent job telling the story of how imaginary numbers entered the mathematical lexicon.
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