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!

about 6 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 8 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.

July 27, 2021 at 12:01am

#1014474

Pennies from Hell

And now, the final entry for this round of "JAFBG"

[XGC]. Tomorrow, I'll go back to riffing on links I found. I have a bunch in the queue now.

What stereotypes accurately describe you? Are you comfortable with them? Which would you like to change?

When I was a kid, once the other kids found out I was Jewish, they'd drop pennies near me to see if I'd pick them up.

For a while I resisted, but then I was like "fuck it" (I learned to cuss early, but unfortunately before I learned not to do it in front of adults), leaned into it, and started picking them up.

Their loss was my gain, and as long as they were going to do shit to me for being different, I might as well make money at it.

Naturally, they figured out what I was doing and stopped. That's when they started asking if Christian babies taste like chicken.

(They taste like pork, but I didn't know that then because my parents tried to keep kosher.) (That's a joke, in case anyone still thinks that bullshit that's been making the rounds for centuries is true. Think we can eradicate fake news? Think again.)

Anyway, these days, no one would know it if it didn't come up in conversation every once in a while. I'm not in the least bit ashamed of my heritage, but it's not like I'm a vegan or do Crossfit and have to shout it to the world. I look like an ordinary Euro-American middle-aged man, and I abandoned religion long ago. After all, it leads to pernicious misinformation; see above.

No, I'm a white guy with facial hair who loves craft beer, and that's a stereotype I can live with. I walk into a brewery and usually I think people look up and go "Oh, hey, it's a beer guy." And yet I don't identify with most of melanin-disadvantaged America. People have tried to start up conversations with me about how wonderfully magical and holy Trump was, and I just steer the conversation away from the political realm. After all, the guy doesn't even drink beer; how could I trust him?

Personally, I think we'd all do well to get rid of the whole stereotype thing altogether. Even the positive ones can be degrading. You end up seeing people not as people but as representatives of a subgroup: women drivers, Blacks eating fried chicken, Jews hoarding money, Scots hoarding money (but for some reason it's a positive trait for them), the Irish drinking a lot, white people who can't stand anything spicier than mayonnaise, Mexicans who only eat spicy food, Asian math whizzes, Roma stealing everything that's not nailed down, the French scowling at anything that's not French, Canadians saying "sorry" a lot, US Americans shooting everything in sight, and so on.

Just stop already. It's the worst kind of confirmation bias: you see someone exhibiting a stereotypical trait for their subgroup, and ignore the same trait in other subgroups, so it reinforces your prejudices. And we all have prejudices; they're mostly just shortcuts that bypass a lot of the hard work that it takes to really get to know someone.

I still pick pennies up off the street, though. One day I'll buy a Coke with all my found cash, and then we'll see who has the last laugh. Now, where did I put the controls to that space laser?

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