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 3 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 5 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.

September 9, 2020 at 12:02am

#992827

Future Imperfect

What "future self?" This is entirely too optimistic.

PROMPT September 9th

Write a letter to your future self. Write the date you would want to read the letter again at the top of your entry (you can choose how far in the future this date is; One year, five years, twenty years, etc.) What would you want to tell your future self? What would you want to know from them?

To: Me. Date: September 9, 2021.

Hey, asshole. Got that flying car yet? No? Still alive, at least? Well, I'm going to assume that you are and go from there.

Please at least tell me 2021 has been better than 2020 was. Somehow I think I'm going to be disappointed.

But hey, you're starting to get the senior discounts. So at least the movie theater is cheaper. Assuming it's still around; it wasn't looking good as of last week.

Most importantly, though, I trust you've discovered more new and interesting beers. Preferably in Belgium. No, don't tell me you didn't make it to Belgium because the EU is still closed to us plague rats in the US. I don't want to know.

I hope you've at least done some traveling; I shall be quite disappointed if you still haven't moved from this spot except to go to the local purveyors of fine malt beverages, including said movie theater.

I'm guessing Elder Scrolls 6 is still "sometime in the future."

But, you know, I suppose if nothing much changes in the next 365 days, things could be worse. Zombies. Alien invasion. Giant Meteor. The inevitable return of the Old Gods, squamous and rugose.

They could also be better, but I'd rather not think about that. Hope only leads to disappointment; only pessimism can bring happiness. Well, pessimism and beer. Well, pessimism, beer, and some of the movies that are supposed to come out in the next year.

Or, alternatively, maybe you'll come across this entry and have a nice chuckle about just how wrong I was. That would actually please me. As you know, that's the great thing about being a pessimist: you can only be pleasantly surprised.

Crack open a cold one for me. And write back soon.

Regards,
Waltz (from one year ago)

8 Like • Comment • View 5 comments

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