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 21 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 23 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.

January 10, 2020 at 12:04am

#973073

A Day in the Life

PROMPT January 10th

What are some of the routines you follow in your daily life? Do you typically stick to your routine, or do you prefer more spontaneity?

Bit of both.

I've said before that there's nothing I do on a daily basis. For example, while I try to write in here every day, there's a glaring hole in my December records that represents my trip to California and recovery therefrom.

The closest I get to a daily routine is about as basic as stuff gets: eating and sleeping. My current meal plan involves six small meals per day - but I skip occasionally, again due to travel. More, smaller meals works for me for weight loss; it keeps me from getting too hungry. If I manage to hit my goal weight, and I'm under no illusion that I can be any more successful at that than I am at anything, that will probably change. And while, like most people, I tend to sleep every day, it's not on a fixed schedule; I have the luxury of going to bed when I feel like it, again with a few exceptions.

One thing I have managed to do on a daily basis is language lessons on Duolingo. In an attempt to keep up a streak, I've managed to at least do a few lessons every day since late August. Until I've been at that for a year, though, I can't say I do it every day.

And then there's exercise. I try to hit the gym every day, but some days, especially when traveling, I just walk for half an hour or more. Rarely, I just don't have opportunity for any dedicated exercise. But I'm determined to not make excuses, so probably 99% of the time, some sort of exercise gets done. Someday, I will fail. Today is not that day.

As for spontaneity, I find that difficult on a daily basis now, but it manages to crop up sometimes. The problem is that most "spontaneous" things I want to do involve calories (e.g. food or beer), so I've forced myself into a schedule to help me stay on track. But when I travel, I often pick things to do and see at random.

Contrary to popular belief (one that I, admittedly, foster), I don't drink every day. Well, water, yes. And Crack Zero, certainly too much. But alcohol consumption is maybe once a week at most.

So, when I'm home, and there's nothing particular scheduled, it goes something like: Wake up whenever; shower; breakfast; cat feeding; language lessons; second breakfast (thanks, J.R.R.); exercise; lunch; other obligations; nap; cat feeding; snack; entertainment; blog; light dinner; reading; late-night snack; sleep. Repeat as necessary. Somewhere in there, I find the time to hang out here and keep up with other things on the internet.

You'll note there's no "work" involved; being retired has its benefits, and besides, work was interfering with my video game time. When I was working, I barely had time to get anything else done. You think it takes 8 hours, but it always ended up being way more than that, especially when I was running the show.

And yet, I never seem to have time to do everything I want to do, or "should" do. I find this frustrating. But I guess that's what life is: compromise.

Woke up, fell out of bed
Dragged a comb across my head
Found my way downstairs and drank a cup
And looking up I noticed I was late
Found my coat and grabbed my hat
Made the bus in seconds flat
Made my way upstairs and had a smoke
And everybody spoke and I went into a dream

8 Like • Comment • View 10 comments

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