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:

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.

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.

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

1 Like

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.

2 Like

December 26, 2020 at 12:02am

#1000835

Rage and Out-Rage

"30-Day Blogging Challenge ON HIATUS" [13+]:
26. National Whiner's Day
Whiner or winer... you pick.
Maybe you'd like to whine about wine...
Or perhaps you forgot to mention a grievance from Festivus...

See? Another pun opportunity today. Though I maintain that Boxing Day shouldn't share the stage. Not gonna whine about it, though. I'm tempted to ask who the one single whiner is, but I should know better than to expect people to use apostrophes correctly. (That is the actual official name of the day; I'm not ragging on the prompt, here.)

Of course, I don't whine. I rant. What's the difference? When I do it, it's ranting and should be encouraged. When other people do it, it's whining and needs to stop. This is similar to the distinction Mel Brooks makes between tragedy and comedy: “Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die.”

I do like wine, even if I do spend more time writing about beer. As with beer, though, my tastes in wine are somewhat iconoclastic. You won't tempt me with a Chardonnay or a Cabernet Sauvignon; those are too ordinary. Give me a Vouvray or a Mourvedre instead. But still, I'm not going to whine about wine, especially if it is free or cheap. (Usually, it isn't.)

Curious about National Whiner's Day,

I looked it up and Thor's balls is it awful.

Coming the day after Christmas, some may think that National Whiner's Day was created so that people can whine about the presents they didn't receive.

Never even crossed my mind.

But that is not the case at all! National Whiner's Day was created by Kevin Zaborney in 1986...

Who?

Oh, this guy apparently goes by Hugambassador on Twitter. As we said in 1986, "Gag me with a chainsaw."

"to encourage gratefulness for what we have rather than what we do not."

Make that two chainsaws.

It is not a day to whine, but a day to be thankful for all that is good in our lives.

Stress level approaching critical zone...

Zaborney also created National Hugging Day, because he believes there are far too many whiners these days, and not enough huggers.

Because of course he did and of course he does. Hey, how's that hugging working out for ya this year, dude? Hard to hug on a Zoom call, isn't it? WELCOME TO THE CLUB.

The day is best celebrated by expressing gratefulness for everything you have...

If you're the kind of person who is inclined to express gratitude, you don't need a day for it. If you're not, you're not going to start just because someone declares there's a day for it. Besides, don't we already have Thanksgiving?

Zaborney also suggests a few other ways to celebrate the day:

I can think of a few suggestions, but let's see what the founder says.

go to a store and observe whiner's returning their holiday gifts

That would involve me going to a store on the day after Christmas, which is third of my Top Five Days Not To Go To Stores, right after Black Friday and Christmas Eve, and right before Third of July and Every Other Day Of The Year. Also, that apostrophe is making my eyes twitch; it's even more egregious than the one in the name of the day.

invite people over for a "whine and geeze" party where non alcoholic wine and cheese are served; have them bring over a gift they want to whine about, that can be used in a white elephant gift exchange; or hold a whining contest

NON-ALCOHOLIC?

Truck away with that bullshit right now. We're supposed to express gratitude, and topping THAT list for me is anything with ethanol in it. Well, almost anything. Anything that doesn't suck but has alcohol. Also get the fuck out of here with the white elephant shitpile that I ranted about in here some time ago. How long ago? I don't know. Recently.

Wow, look at that. I started this entry in a pretty good mood

, and now I'm about to pop a blood vessel.

Better grab some wine.

But first...

Mini-Contest Results!

Seriously great, creative No-"L" entries by everyone yesterday! It was hard to pick a winner, and while the temptation is there to give everyone a Merit Badge because it is, after all, Chri- OH WAIT, it's not Christmas anymore, so there's only one Merit Badge. But I did appreciate everyone's really supremely clever L-less descriptions, and you will all get another chance at an MB before too long. Maybe even New Years Eve if I can remember to do one that day (for obvious reasons, though, the New Years Day entry, and thus any award, might be delayed).

But for today, Kåre เลียม Enga

will get a Food Cooking MB because I, too, am a fan of stuffing. Of course other people mentioned stuffing, too; like I said, it was a close one all around. Thanks for the comments!

7 Like • Comment • View 3 comments

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