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.

May 19, 2019 at 12:23am

#959246

Idealized

Write about your ideal weekend.

One of the many great things about being me is that every day is a weekend day.

Alternatively, you could say that I have no weekends, but despite my pessimism, I prefer to think of it as the former.

I do pay attention to what day it is - it helps to have an idea of what business are open at which hours, and if I can expect to deal with traffic if I have to venture out. So, yes, I'm aware that it's Saturday night and I've once again spent it sitting at home watching Netflix and taking care of some stuff here on WDC. When I go out, I tend to eat bad (but delicious) food and drink alcohol, which are two of my favorite activities, but I'm still committed to losing weight and those activities are anathema to that.

Now, if I did those things every day, I'd say that my ideal weekend would be a break from it. But since I don't - well, I do eat food (almost) every day, but it's low-calorie fare, and I drink maybe 2-4 times a month now - then my ideal weekend would involve eating pizza and getting drunk.

For the record, that's been my ideal weekend for as long as I've been drinking.

Since we're talking Platonic ideals here, I might as well throw in gambling, also. But, again ideally, it would have to result in only a small loss of money - just enough to call it an entertainment expense. If I'm not in a casino, though, any kind of gaming is fine - video, or playing D&D with friends, or whatever.

What I'm doing now - restricting my activities in hopes of a beneficial result in the future - well, that's not the kind of thing I usually do. It feels like a foreign country. Instant gratification is more my thing, as nothing I've ever actually put effort into has ended up being worth the cost.

It might be important to note certain things that I'm sure would be a part of some others' lists, that are conspicuously absent from mine:

Fishing

Hiking

...really, any outdoor activity

Anything remotely productive

Sex

Catching up on sleep (no need)

Shopping

Consequently, my ideal weekend would be in a casino in Vegas (one with good restaurants and great drink selection, which is most of them), never venturing outdoors, and not losing too much at blackjack. However, weekends in Vegas tend to be too crowded for me, so I'll declare the weekend to be Monday and Tuesday for my purposes.

I'm thinking maybe sometime in August.

2 Like • Comment • View 3 comments

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