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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 hours 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

about 3 hours 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.

May 18, 2023 at 6:11pm

#1049803

Legally Binding

While one should never get their legal advice from an online comedy site, you might like this Cracked article about laws.

5 Uniquely American Laws That Other Countries Don’t Seem To Need

Yeah, I don't know if these are unique. And it's not like other countries don't have stupid laws, too. Hell, some of them still punish you for blasphemy.

The United States is a pretty weird country.

Which one isn't? Oh, yeah, Canada. Never mind.

Even though what’s supposed to be the famous, usually screamed tenet of America is freedom, the actual freedoms we do and don’t have are cherry-picked and puzzling.

Yeah, right. "Freedom."

So it’s unsurprising that there’s a whole lot of regulations and laws in the U.S. that haven’t fallen far from the apple tree — at best confusing, at worst fully oxymoronic.

Or just moronic.

Here are five American laws that are likely, in the eyes of other modern governments, incredibly dumb.

I always liked those lists of weird laws still on the books, like needing a license to wear penny loafers, or whatever.

These aren't those, though.

5. Female Lawmakers’ Backwards Dress Codes

Another point on the high school side of the scale is the fact that, despite being our chief legislative body, Congress still enforces a fucking dress code. And like most dress codes, it’s a whole lot more draconian when it comes to the female members.

That's idiotic, sure, but then there are still countries where "female lawmaker" is semantically and legally impossible.

Sure, Britain isn’t much looser, but they also think “fanny” is a cuss, so is that such a win?

That's what I've been saying.

4. Kinder Surprise Eggs Banned

Another common feel in American law is the conflict between a country that’s supposed to be advocating for freedom above all, while seemingly convinced that every American has the death drive of a baby lustily staring at the forbidden liquids beneath the sink. One place this pops out is in the absence of the Kinder Surprise Egg in American stores.

Meanwhile, far more hazardous products remain legal. You know what I mean.

3. Weird Real Egg Laws

Right, because no one else has weird laws about food.

2. Pharmaceutical Advertising

Everywhere else foolishly believes that if you need medication, your doctor probably isn’t relying on you to provide suggestions. It doesn’t help that the advertising is just as predatory as usual, mostly suggesting that if you don’t fix your allergies, your child will spit on you and leave you to cry in a musty robe while they go to the park to play with their other parent, who they now like more.

I despise almost all advertising, and it is kinda strange to push prescription medicine on the TV, but there are worse things to advertise. Homeopathy, e.g.

1. Sex With A Porcupine

And I'm done with the internet for today.

6 Like • Comment • View 2 comments

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