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 24 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

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.

December 28, 2019 at 12:16am

#972128

Open and Shut

Nothing intellectually challenging today. Just an interesting bit of trend reporting.

https://www3.bostonglobe.com/metro/2019/03/06/miss-walls-cry-for-help-from-woman...

People in open-concept homes are realizing the walls were there for a reason

When Star Trek premiered on TV back in the 60s, camera equipment was bulky as hell. Ever wondered why the corridors were about five times as wide as they needed to be? It was so they could track with the cameras. It doesn't make sense that there would be wasted space on a starship, but that show, more than any other, has informed our ideas of what a spaceship should look like. Contrast that with the 1960s reality of space capsules smaller than the cars of the period.

I mention this because I'm pretty well convinced that open-concept housing became so popular because it's easier to display on TV.

“In our old house,” said Didonna, a financial analyst, “I’d come home and make dinner and my husband would be watching TV in the other room, and a good portion of the evening we’d be apart.”

She got her togetherness, all right, in a glorious new house in Millbury. Now when she cooks and her husband watches TV, he’s in full view. Relaxing. While she works. “Frankly it’s annoying,” she said. A real estate agent has been called.

“I miss walls,” she said.

You probably also miss actually communicating with your spouse. Real estate agent? You lot need to call a marriage counselor. I say this with great hypocrisy; I've been known to sit back and smoke a cigar on the front stoop while watching my wife mow the lawn (in my defense, I had a bad back). Now I don't have a wife. I don't fail to see the connection.

I think our ideas of how we're supposed to live pretty much come from popular culture. And like I said above, some of these things just track better on TV. It's easier to film a scene where one person is cooking and the other is sitting on the couch if you can do it in one shot. It's also cheaper to do set design with fewer props, and so the "uncluttered" look became the ideal.

Is it "life imitates art" or "art imitates life?" I can never remember which was the original platitude and which was the parody.

Honestly, I vacillate, myself. I've lived in the same house for something like 25 years now - much longer than I lived in my childhood home - and not only do I like the house, but I like the neighborhood and I like the city. Every time I think of living somewhere else, I think of all the things I have here and go, "...nah." And yet I yearn for the unfamiliar at times, which is why I travel, and it's also why sometimes I think about what it might be like to live elsewhere.

If I did, though, would I want an open-concept design, or a partitioned one? I don't have kids, so family time isn't a consideration. I do have friends, and I've been known to host parties at my place, and open-concept would work for that. I'm also quite a lousy housekeeper; I like my stuff (I say again, fuck you, Marie Kondo), and I have a lot of stuff. I'll never conform to the Spartan ideal of minimalist living. So having extra rooms just to keep all the stuff in would be nice.

One thing I'd never do, though, that I find extraordinarily amusing: the "show kitchen." It reminds me of the WASP habit of carefully furnishing a living room, say, and then never letting anyone so much as set foot in it for fear its museum-quality pristine shine would be tarnished by an errant footstep denting the carpet. I remember visiting such people when I was younger, and they were always quick to show me the precisely arranged "living" room whilst barring entry to its sacred space. Seemed to me like a waste of money and room. So it is with the show kitchen.

But hey, whatever works for you. I do reserve the right to snark about it.

2 Like • Comment • View 3 comments

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