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  1. A Visual, Intuitive Guide to Imaginary Numbers

    • Negative numbers aren’t easy. Imagine you’re a European mathematician in the 1700s. You have 3 and 4, and know you can write 4 – 3 = 1. Simple. But what about 3-4? What, exactly, does that mean? How … See more

    Enter Imaginary Numbers

    Imaginary numbers have a similar story. We can solve equations like this all day long: The answers are 3 and -3. But suppose some wiseguy puts in a teensy, tiny minus … See more

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    Visual Understanding of Negative and Complex Numbers

    As we saw last time, the equation x2=9really means: or What transformation x, when … See more

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    Finding Patterns

    Let’s dive into the details a bit. When multiplying negative numbers (like -1), you get a pattern: 1. 1, -1, 1, -1, 1, -1, 1, -1 Since -1 doesn’t change the size of a number, just the sign, yo… See more

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    Understanding Complex Numbers

    There’s another detail to cover: can a number be both “real” and “imaginary”? You bet. Who says we have to rotate the entire 90 degrees? If we keep 1 foot in the “real” dime… See more

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