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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Brandiwyn🎶

a day ago
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.

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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.

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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.

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

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November 1, 2021 at 12:02am

#1020504

Bare Necessities

Well, it's November. Two more months until the end of the year. Somewhat less than that and, if nothing catastrophic happens, I'll have written in this thing every day for two years. Hey, I don't have many accomplishments in life; give me that one.

For those of you peeking in for the first time from the November edition of "30-Day Blogging Challenge ON HIATUS"

[13+]: Hi, I'm Waltz. This is my blog. I'm a dedicated indoorsman and I live an alcohol-positive lifestyle.

PROMPT November 1^st

We all have possessions of some type. Tell us five possessions you can’t live without, and why they are on this list.

I'm just going to go ahead and assume this is metaphorical and not literal, otherwise everyone would be like "air, water, food, clothing, shelter," and that would be boring. I'm also going to exclude consumables such as beer, which is only in my possession for a few minutes before it becomes a part of me; and also semi-sentient entities such as cats and friends. But the funny thing about possessions is that, often, we think we can't live without them but it turns out life goes on when they break, someone steals them, or they run into a deer and get totaled. So without further ado, The Five Possessions I Can't (Or, Technically, Wouldn't Want To) Live Without.

5. House

Yeah, yeah, I know, that's part of the "shelter" necessity above. But while "shelter" in general may be a necessity for human life, I'm talking about my house in particular. I acquired it half a lifetime ago, and it's paid off, so it really is my possession. It's about the right size for me and a housemate and the cats; the location is terrific (I can easily walk to at least four different bars and stagger back); and it usually doesn't leak. While I love to travel, I don't think I'd be happy living anywhere else for an extended period.

4. Laptop

I spend most of my waking hours on the laptop -- writing, working, learning shit, playing video games, watching shows and movies, laughing at cat videos. I could probably get by without my dumbphone, but not the laptop. It's getting old now and probably needs to be replaced soon, at which point the new laptop will be what I can't live without. In other words, it's not necessarily this computer, but a computer that I need to lead a fulfilling life.

3. Chair

Really, almost any chair will do as long as it's not too uncomfortable. A chair is essential for #4 above. Standing while using the computer would get really old really fast.

2. The Bed

When I'm not on my laptop (or at a movie theater or bar), I'm in the bed. It's comfortable and adjustable so I can sit up and read in it. Since I spend at least a third of my life there, it makes the list.

1. Money

Of all the things on this list, this is the most important (hence its position at #1; I'm stealing the format from Cracked here and doing the whole countdown thing). Why is it the most important? Obviously, because if I ever found myself in the position of being without any of the above things, or the 99,996 other things I don't want to live without, money would be there to replace it. So really, of all the things on this list, it's the one thing I truly can't live without.

"But Waltz, money can't buy happiness!" Maybe not, but it can buy beer, and that's good enough for me.

There are, of course, myriad other items that could have made the list: books, water heater, stove, toilet, refrigerator, washer/dryer, plunger, shower curtain, sunglasses... life would be annoying and/or boring without a lot of that stuff. And this is one reason why I am not, and don't think I ever could be, a minimalist.

I have managed to live without a car for four months now, though, so you never know.

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