My Latest Math Obsession- Imaginary Numbers

Okay, these probably sound kinda spooky or weird, but I am coming to adore imaginary numbers. After having them on this online test, I inquired with my math teacher, who taught me about them. And now I’m in love! They’re so weird and out-of-the-ordinary. They are nothing you’d see in day-to-day arithmetic. My math teacher struggled to explain how they’re even used. But the properties of them just astound me. I love them. 

The basics of i is that it’s the square root of negative one. Then, depending what power it is raised to, the value of it changes. See description below:

Image

 

It repeats in a pattern like this so i to the fourth power is just one again. Then you can multiply binomials containing it to simplify. Like this, (1+2i)(3+4i). You use the standard Distributive Property, and end up with 3 plus 6i plus 4i plus 8 times i to the second power (this is much easier to write in words than to type). Then, you can combine the like terms of 6i and 4i to get 10i. Then, i to the second power is -1, so eight times negative one is negative eight. Combine that with three to get 5. And there you have it! 10i-5 is your final answer!

I have no idea why I’m writing this on a reading-centric blog, but I guess it may be useful if you come across imaginary numbers in something else. I’m also just really excited. I hope you enjoyed the lesson on i!

-Nicole

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