Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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10 Most Recent Blog Comments:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 5, 2019 at 12:07am

#958246

Nothing Really Sucks

Happy Sunday! Take the time in your blog today to reflect on your week. Share one thing you accomplished this week and one thing you hope to accomplish next week.

Accomplishments are overrated. At this point, my greatest accomplishment is "I'm still alive." I hope to accomplish this again next week.

I wasn't always this way, you know. Like most everyone, I had big plans when I was young. Own a company, travel, be able to retire comfortably, own a house, live with cats, write, become a rock star...

Rarely did I stop and think how these goals were contradictory. When one owns a company, one rarely has the time to travel or write. If one travels, one is spending money that could fuel retirement. At least it's possible to own a house and put cats in it.

Thing is, though... I accomplished all of these goals. Well, except for the rock star one. That one I gave up on. Turns out lack of talent is still a barrier to that; who knew?

So, I quit making goals. Well, sort of. I continue to lose weight. That's something, I suppose. And I do have the nebulous and impossible desire to visit every microbrewery in America. Nebulous because it's a goal without a real plan; it's not like I can visit over 6000 breweries while driving. Impossible because, every week, on average, we gain two breweries and lose one. Hell, California alone has over 10% of them; it's all the way on the other coast, and even if I visited two a day it would take me nearly a year just for that state. Maybe it'll finally secede and then it won't technically have breweries in my country.

Still, it's something to shoot for. Just not this week.

This week, then, will be more of the same. Keep myself distracted so I don't eat. Go to the gym. Get some writing done - this blogging activity and other stuff. Oh, and I have a contest to judge; that's going to take a good chunk of my time.

Here's the other thing about goals and plans that I realized a while back: Every time you decide to make a change in your life, you have to give up something. Maybe you want to give up something; that's okay. But say, for instance, I decided I wanted to date again. Then I'd have to give up video game time. I'm not willing to give up video game time; ergo, I don't date.

At some point, I reached a place in my life where I said, "Okay. That's it. That's enough." And it really is enough. Not that I don't want to continue to grow or change, but at this point, nothing really sucks, so why fuck with it?

I mean, "everything is awesome" might be better than "nothing really sucks," but at the same time, "nothing really sucks" beats "life is crap." And making the wrong life decisions ends up in "life is crap."

By the way, the bit about having to give up something to make a change in your life? It works the other way around, too. That is, if you want to give something up - say, smoking or Facebook - you can't really just, you know, give it up. Whatever that activity is, it took time and energy. That time and energy can't be destroyed; it can only be redirected. "I will munch on baby carrots" works much better than "I will quit smoking." "I will read actual books" can lead to less time on Facebook. That sort of thing.

So, nothing sucks. And I intend to keep it that way as long as I can.

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