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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 10 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 12 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.

June 17, 2020 at 12:08am

#985822

Zombie

I ventured Out Into The World for the first time in three months yesterday. Well, unless you count walks to medical offices; I don't because those aren't fun. No, this time, I walked over to the shopping center because I had to pick up a prescription (as a result of one of the trips to the doctor -- not a big deal, just routine), and then I noticed that the nearby taphouse was open for outdoor seating.

It was around 3pm, and the temperature was only around 70F (quite low for a Virginia afternoon in mid-June), so there was no wait. Thus, I was able to have my first (and second, and third) draft beer since mid-March.

It felt almost... normal.

Then I walked home and passed out. And that was definitely normal. Downside to losing weight? Lower tolerance. Upside to losing weight? Cheaper to get drunk.

Anyway, today is entry #5 for "Journalistic Intentions"

[18+]

8. Try not to become a man of Call of Duty prowess, but rather try to become a man of legitimate Zombie Apocalypse fighting skills.
Brandiwyn🎶

I'm not familiar with whatever the original of this twisted quote is. Probably doesn't matter.

Confession time: I've never played Call of Duty. I don't actually know much about it. I'm more of a Bethesda fan: Elder Scrolls, Fallout, that sort of thing. I've heard good things about CoD and its sequels, but just never got the urge to play it.

But I don't think that's the point.

All the joking around we all used to do about the inevitable zombie apocalypse seems rather naive what with everything going on right now. An actual pandemic? Cops out of control in the streets? Yeah, no thanks. The attraction of fantasizing about a zombie apocalypse was that the line between the good guys and the bad guys was really clear. Good guys: not zombies. Bad guys: brain-munching shamblers. You could project all of your hate, fear (they are not the same thing), and prejudice onto the hordes of moldy undead.

Liberal or conservative, warmonger or peacenik, we could all agree that zombies are bad and need to be eliminated. They are, however fictional, the Common Enemy, and (with a few exceptions in movies and whatnot) there's no nuance there. The survivors have to band together, cooperating against an all-encompassing threat.

Even when you have the whole space-alien-invasion trope, there's always, somewhere in the background, the idea that some people will side with the aliens. Not so with zombies. We're all in this together.

Well, recent events have thrown into sharp focus the realization that we're not all in this together, and probably never will be.

So, give me a video game. Preferably one where I can play as a good guy, or as a bad guy, or (my favorite) a bad guy who convinces everyone he's a good guy. Escape from reality? Sure. Have you seen reality?

Three very interesting and well-written answers to yesterday's mini-contest about Why We Are Huge. Though I do have to say I'm just a little bit disappointed that no one proposed "space aliens are fattening us up for the harvest."

So it's close, but this time the MB goes to SB Musing

. Check yesterday's comments for the post; it's too long to comfortably copy/paste here. Thanks for reading and commenting!

I'll try this again sometime soon, though probably with some subject matter that's a little less... weighty.

9 Like • Comment • View 8 comments

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