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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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.

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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 4, 2019 at 12:18am

#958202

Exploring the Unknown

Stand outside for two minutes. Make a list of ten things you can smell, ten things you can hear, and ten things you can feel.

Out... outside? You mean, like... not inside? You want me to go what now?

Fortunately, it is midnight; the accursed daystar is on the other side of the planet.

So, fine, I'll do the exercise.

Ten things I can smell
1. Tobacco smoke. I figure if I'm going to venture into the Great Unknown, I might as well light up a cigar while I'm out here.
2. The remains of the "present" one of my cats left me.
3. Pollen. It's a good thing I'm not allergic, or all 10 of the items on this list would be "nothing."
4. ...Let's just say it's been a few hours since I've showered, and leave it at that.
5. Stinkbugs. To be fair, I smell them in the house, too.
6. Hm, I think one of my propane tanks is leaking. *looks at burning cigar* *shrugs*
7. Damp wood. It just freaking rained. Luckily, it is no longer raining, or I'd be skipping this exercise.
8. I could be imagining it, but I think there's a faint odor of shit, like there always is in the outdoors.
9. Oh, there it is. Some sort of flowery whiff. It is May, after all.
10. Petrichor. This is one of my favorite words, and it's all thanks to Doctor Who.

Ten things I can hear
1. My cat scratching at the door. I'm outside, so she needs to be, too. She doesn't realize it's wet.
2. Cars. Generally, in every direction, but mostly from the interstate about a mile south of here.
3. Moths trying to commit suicide on my deck light.
4. Meow. Cat's getting insistent; I think I'll go let her out.
5. Creak. Clearly, I need to oil some hinges one of these days. I've been saying that for 23 years, now.
6. The backyard neighbor's stupid fucking dog is howling again.
7. Okay, something just crashed through the underbrush in the backyard. Maybe it's a bear. Or a mountain lion. It's not a skunk; see above.
8. Next-door neighbor's heat pump just kicked in.
9. Loose water is dripping off the leaves and splattering.
10. I have no idea what that squealing noise was, but I'm pretty sure something just died.

Ten things I can feel
1. Trepidation.
2. Wet.
3. Cold.
4. A creepy, crawly sensation down my back. Oh, yeah... spider.
5. Lost, because I'm not indoors.
6. Moths crashing into me when they get bored with the light.
7. Some unidentified bug on my ankle. This is why I hate the outdoors.
8. A scraping sensation where I swatted said bug off of my ankle with my left shoe.
9. The overwhelming desire to go back inside.
10. The bottom of my laptop as I carry it back in.

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