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 22 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 15, 2020 at 12:01am

#973424

Honesty

PROMPT January 15th

Write your entry today about commitment. Committing to an activity, craft, person, way of being, etc. Consider the concepts of diligence, honesty, and responsibility. What does commitment look like to you?

The inside of a padded cell.

I mean, really, English? Using the same word for these two concepts? "I was committed" has two possible meanings, distinguishable only in context.

As with being confined to the room with the plush walls, though, the other kind of commitment can be stifling - depending, I think, on whether you choose it or not.

If you've been following along, you might get the idea that I'm afraid of commitment. And you wouldn't be entirely wrong. We should be afraid of it. It should instill a mighty fear, one that would keep us from entering into covenants without due thought and consideration.

I do fear having commitment thrust upon me without my full consent - because I take it seriously, and will do everything in my meager power to fulfill one.

"But you've been divorced twice, Waltz!" Yeah... her idea both times. I wanted to keep my commitments.

It's true I didn't want to have kids, but I chose partners accordingly. One of them went on to have one anyway. Good kid. Nothing at all like his deadbeat dad who wouldn't recognize an obligation if it hit him upside the head. Her choice, though. If I'd had that responsibility handed to me, I'd have done whatever I could to be a good father. It's just that I didn't want to be a father, so instead of spreading my seed around like a firehose, I took precautions. That's also responsibility.

I wish I could say that I've always done everything I promised I'd do, but I'm far from perfect; I've slipped. But I try to do so. Promises to myself fall by the wayside faster than promises to other people; like anyone, I've failed at following through on goals. But when there's another person involved, I do my best to be diligent.

So I choose my commitments carefully. That's not avoidance; that's just knowing my limitations. I can take care of cats just fine, but I'd grow to resent the constant demands on my time that dogs represent. Hell, I can't even keep a houseplant alive. Seriously. No matter what I do, they always wither and die. And I spent my childhood growing vegetables on a farm. I once decided to get an oregano plant, because I put oregano on a lot of things and fresh is better than dried. It took two days before it was brown, brittle and droopy. Yes, I did water it.

Don't ever trust me with a houseplant is what I'm saying. I have a black thumb. Somehow I manage to do okay by my cats, though.

If you search for tenderness
It isn't hard to find
You can have the love you need to live
But if you look for truthfulness
You might just as well be blind
It always seems to be so hard to give

Honesty is such a lonely word
Everyone is so untrue
Honesty is hardly ever heard
And mostly what I need from you

7 Like • Comment • View 6 comments

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