What are complex numbers, also known as imaginary numbers? It turns out that these numbers are more real than the so-called real numbers! How is that possible? How were complex numbers invented? What are they used for? What are quaternions? We will talk about this with dr. Tomasz Miller in the Code Universe series. We invite you! TABLE OF CONTENTS: 00:00:00 Introduction 00:02:09 How were negative numbers discovered? 00:14:06 Why do we need complex numbers? 00:20:49 What are imaginary numbers? 00:28:53 How were complex numbers invented? 00:34:55 The first formulas of complex numbers 00:46:35 Complex numbers in the third dimension. Quaternions 00:58:52 Future uses of octonions 01:02:47 Conclusion ???? Join the Astrofaza CREW! ⤵️ Crew members in the form of ???? Patrons and ???? Supporters on YouTube help us create even better content and publish it more often. If you also want to help us create the best version of Astrofaza, you can do it in several ways: ❤️ Become a Patron and join a closed group on Facebook, with faster access to some content and many additional bonuses. ✔️ Patrons also gain access to additional content for supporters from the Senior Officer threshold (PLN 9.99). ????PATRONITE - http://patronite.pl/astrofaza More details on the profile in the link. ❤️ Join Supporters on YouTube. In a special section for supporters you will find additional materials available only to them: ✔️ episode expansions, ✔️ additional live streams, ✔️ behind the scenes materials and hidden posts. ✔️ And as the cherry on the cake: a badge with the Astrofaza logo next to your nickname in the comments and the ability to use special Astrofaza emojis! ???? / @astrofaza ❤️ T-SHIRTS, SWEATSHIRTS, PILLOWS, MUGS and other Astrofaza gadgets at AstroSzop. If you want to have an Astrofaza gadget, it will also help us develop our channel ???? http://astroszop.pl​ ???? Still not enough Astrofaza? Be sure to check out our social media! ???? ✔️ INSTAGRAM - More behind the scenes materials and Astrofaza more privately ➡️ / astrofaza.pl​ ✔️ FACEBOOK - Information about our activities added on an ongoing basis. ➡️ / astrofazapl​​ ✔️ DISCORD - Astrofaz's place for cosmically crazy people. You can't help but check it out! ➡️ / discord ✔️ ASTROMISIE Group - Talk to the rest of the crew ➡️ / astromisie ✔️ Command center - http://astrofaza.pl​​ ✔️ ASTROFAZA'S SECOND CHANNEL - / astrochillout​​ ⚠️ If you like it, don't forget to like and sub if you haven't already. ⚠️ And if you're already subscribed and don't want to miss new videos, click the bell next to the subscribe button. You can also click below: ➡️ http://youtube.com/c/astrofaza?sub_co... THANKS AND HAVE A NICE FLIGHT!???? ???? TEAM ???? host: Piotr Kosek and dr Tomasz Miller photos and production: Kamil Ziółkowski editing: Dorian Ortyński ???? MUSIC ???? The Astrofaza channel is the largest channel in Poland, whose topics are space, astronomy and future technologies. Here you can also watch our popular science program POP Science with dr hab. Leszek Błaszkiewicz, in which we cover topics such as: Aliens and alien civilizations, grandfather's paradox and time travel, faster-than-light travel, etc. We invite you!