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').

1 Like

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.

July 13, 2019 at 12:07am

#962521

Rather Not

Have fun answering these “Would you Rather?” questions in your blog today! You can choose to answer as few or as many as you like

Would you rather live a boring, long life or an exciting, short life?

I think my life speaks for itself there. Sadly, it's turning out boring and short. But considering how my parents went, I'll take the Neil Young option: it's better to burn out than to fade away.

Would you rather be able to fly or teleport?

Like I said before, for me it's about the journey, not the destination. Fly, definitely. Well... depending on how fast. I had a story idea in mind where someone wished they could fly, and the dickhead genie grants the wish, letting them fly at a slow walking speed. That would suck. Genies are assholes. I've wasted way too much time, usually whilst drunk, trying to get the perfect wording down for wishes, and then promptly forgot it when I sobered up.

Would you rather be able to only time travel to the past or only time travel to the future?

The past sucked syphilitic balls. Shit everywhere, plagues, superstitions, poor hygiene, short and brutal lives, no internet. No thanks. I know a lot of people romanticize the past; hey, if all of that works for you, great. I suppose there would be one benefit: I know enough about how some things work to "invent" a few minor contraptions (though with my luck, it would get me executed for witchcraft). Still, assuming I'd have to go back more than 100 years or so, the infrastructure wouldn't be there to run washing machines, produce Coke Zero, or refrigerate food. Worst of all, no air conditioning. Shudder. At least there would be beer. Warm beer, but beer. That is, unless I had to go way back, in which case I'd probably be promptly swallowed by a tyrannosaurus rex, or get chomped by a spider the size of a truck. So... no, thanks; you can keep the scary-ass past.

Now, there's always the chance that the future will be just as bad or worse. If some catastrophe kicked us back to the Stone Age, we'd be utterly fucked, because all the easy raw materials are gone. Ever seen a raw flint nodule? No? Me neither, because our ancestors flaked them all into murder weapons. Regardless, I'd rather take my chances in the future, just to see how it all turns out.

Would you rather lose your hearing or your sight?

Seems to me I've answered this before. Something like 75% of what I hear is annoying, distracting, grating, or frustrating. Unfortunately, the other 25% is music, without which I wouldn't want to live. But I need eyesight to play video games, also without which I wouldn't want to live. Tough call, and one I don't want to make. Pass.

Would you rather live the rest of your life as a cat or a dog?

No. They both lick their own assholes (I know some people would call that a bonus), eat disgusting things, and don't drink beer.

Still, if I had to choose, it'd be cat, no question. They sleep more, and eventually they will achieve world domination, and if I'm going to be there for that, better to be there as a cat.

3 Like • Comment • View 6 comments

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