Tag: imaginary number

  • Our Number World

    Our Number World

    This is a math story, but the names have been changed to protect the innocent.

    UPDATE June 2026: When going back through content on MathFour.com, I read through this and it took me a while to figure out what the heck I was writing. If you start reading this and feel like you’re confused, try using this word unscrambler tool for the proper names in this story.

    There once was a strange little world called Lears. It was quite small, relatively speaking, and had only one continent. The residents called the continent Tailorsan and they named the single ocean (with all its very strange fish) Ralitanisor.

    In Tailorsan, there was a single city called Egrestin. Anyone living outside of the city was called a “mice lad.” (People weren’t very nice to those country folk!)

    All the Egrestins lived happily in Egrestin, it seemed. At least until one day…

    Crime set in!

    There was a group of Egrestins who didn’t seem to like anyone. They would meet regularly and fight. Everything they did was hateful and mean.

    So the more optimistic and positive of the Egrestins began to migrate to one side of the city. Soon they decided to form an official, and gated, neighborhood.

    They held a contest for the name of their new community and Mr. Reoz, a very liberal man, won. He had chosen “The Lehow Urbsmen.” (A rather fancy name, but they were the snobs of the city.)

    “That outta keep out the rubbish,” Mrs. Neetiff said to some of her neighbors as they finished the gate around their shiny new community.

    Mr. Reoz overheard her and was horrified.

    “Mrs. Neetiff. I understand that we don’t want crime in our neighborhood,” said Mr. Reoz, “and we don’t like all the negativity. But the people outside of The Lehow Urbsmen aren’t ‘rubbish’ — they’re people too!”

    She responded, “Well, how about this, then… why don’t you move outside our nice little community!?”

    Mr. Reoz looked at her and thought about it. He never liked her much — and she was so odd.

    He said, “Since I picked the name for the community, I don’t really think that’s right. But I’m not sure I want to live inside the gate with the likes of you!”

    So they rebuilt the gate to exclude Mr. Reoz’s house. He remained a part of the The Lehow Urbsmen, but just not inside the gate.

    He named the gate “The Alasturn” — a word that means “The Optimists” in the Learsian language. He hoped that giving them that name would have a positive effect on them.

    He became the middle man.

    Mr. Reoz eventually became friends with everyone in Egrestin. In his networking, he was able to introduce people from inside the Alasturn to other Egrestins.

    It seemed that through him, each member of the gated community perfectly matched someone outside of the community.

    And they lived happily ever after!

    Can you draw the map of Lears? What does this have to do with math? Did I miss anything?

    Share your thoughts in the comments or on twitter/x.

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  • Using Conjugates in Imaginary and Complex Number Work

    Using Conjugates in Imaginary and Complex Number Work

    Complex numbers are made from one part real number and one part imaginary number. That’s one heck of a mixture.

    Anytime you mix things, you take the complicated to, well, the complex. (Goodness I’m punny today!)

    We use conjugates in the manipulation of these things. First it’s important to understand what a conjugate is…

    It’s just a pixie-dust quick-switch sleight of hand thing, right? Pretty much. Can you legally do that? Well, no. Clearly 4+8 is not the same as 4-8. Anymore than 12 is the same as -4. Duh.

    But you’ll see in this next video that you’re not really jumping up and trying to change the value of things…

    What’s really happening is that you’re inventing something to use as a “clever form of one” – the big fat one.

    And here’s one more example. Don’t forget to comment if you’re still confused.