Imaginary Numbers Are Real [Part 1: Introduction]

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Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.

Part 1: Introduction
Part 2: A Little History
Part 3: Cardan’s Problem
Part 4: Bombelli’s Solution
Part 5: Numbers are Two Dimensional
Part 6: The Complex Plane
Part 7: Complex Multiplication
Part 8: Math Wizardry
Part 9: Closure
Part 10: Complex Functions
Part 11: Wandering in Four Dimensions
Part 12: Riemann’s Solution
Part 13: Riemann Surfaces

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32 thoughts on “Imaginary Numbers Are Real [Part 1: Introduction]

  1. Remember mathematics is racist. Not only is Gause white, he was german, and all germans are nazis. As woke self hating white liberal, I demand these racist numbers be replaced seminars on inclusiveness and cultural sensitivity. Only after we get rid of the legacy of such racists as Leibnitz, Gause, and Newton and remake mathematics using the ideas of nonbinary non-white mathematicians can we end the systemic cultural racism that exist in the realm of numbers. Numbers are racist

  2. The fact that we considered "imagination" isn't real so that leads to this type of numbers as well
    so how about we accept one weird reality that imagination is real in some sense

  3. Blääääää😥⚀tuossa nyt nätisti mut käytänössä optiikka tieten muuttaa tuota lateraalia ja jne…

  4. imma just gonna start making up mathematical concepts, seems to work. I'll invent a number Q that instantly solves any equation. QED

  5. lateral living in the time of gauss, ill ask him how he realise about those things, if it is a genius thing or is something that came from lateralation.

  6. So does that mean my imaginary girlfriend is real?

    Jk I don’t have one but I had to make this comment.

  7. I'm not saying lateral numbers don't exist, but at least all other numbers exist elsewhere in the universe. Whole numbers are obvious. Fractions are just parts of something, say pie. Some irrational numbers are naturally occurring, like pi, e, the squareroot of 2, etc. although I lack the words to describe it well.
    And even negative numbers exist, with antimatter, which when added with normal matter, makes both disappear, just like when we would normally add -1 and 1 together. Thus also zero exists.

    So there are really just 3 options:
    1: Lateral numbers are imaginary.
    2: We simply haven't discovered the real lateral numbers.
    3: Lateral numbers are an exception to the rest of numbers (this is really just an excuse to not say it's imaginary)

  8. wow man your explanaition is brilliant i saw it for the first time and understood it very well when its still from a grade a lot ahead of me thanks . and keep the good work up cuz your great in this

  9. "Imaginary numbers" is a fine term. The trouble lies with our disparaging colloquial usage of the word "imaginary." We often use it as a synonym for "fanciful" or "impossible," when, in reality, it is a perfectly respectable word.

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