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:

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

September 30, 2021 at 12:03am

#1018365

Wake Up Now

It's the final day of September, so I thought I'd take a break from trolling internet articles to do some personal updates and plug a few friends. Er, I mean, plug a few friends' items here on WDC.

Home Ownership

By which I mean, the continuing process of being owned by a home.

Last week, in "Hard, Erect Deck"

, I detailed some of the tribulations involved in replacing my house's back deck. Basically, I'd put it off as long as I could, but the old one was about ready to fall over, most likely with me on it, so this was much-needed home maintenance. However necessary it was, though, neither I nor the cats took kindly to the change. Now, though, it's about half done, with the entire superstructure in place; they still have to do some electrical work to put in some lights and outdoor outlets, and finish up the drainage system. But here I am, tonight, sitting on the new deck getting cancer from the treated lumber fumes.

It rained some last night, and I took great pleasure in being able to stand, dry, on the patio beneath and watch the drainage system in action. Said pleasure was mitigated somewhat by watching the trees in the backyard sway in the thunderstorm's stiff breeze. I don't want one of those trees to fall onto the brand-new deck (or, you know, my house) in the next windstorm, so I guess my next project is to cut down some trees. Let me rephrase that: my next project is to pay someone to cut down some trees (the ones in question are nearly dead anyway).

The only downside to the new deck is that my cats were accustomed to leaping up to the old one from down below. They can't do that now because the new railing is too dense for even a cat to get through. Something about building code changes. I told the contractor this yesterday, and he volunteered to use some scraps to put a cat ledge on the outside so they can jump to that, and thence onto the rail. He also reduced the price somewhat as lumber prices have come down since we signed the contract. I like this guy so far and will probably hire him for other work; sadly, he doesn't do trees.

Meanwhile, some pipes broke in the house so now I have to deal with plumbing issues as well. It never rains but it pours. In this case, it pours discharge from the dishwasher through a cracked pipe. So I also have to clean up that mess. Fortunately, I got the worst of it fixed yesterday, so at least I can run the dishwasher.

Bite Me

Went to the dentist yesterday for a routine cleaning. He found work he says needs done. I was like, how much. They showed me. I nearly had another heart attack. Which would be expensive and probably fatal, but at least then I wouldn't have to take out a mortgage to get my dental work redone.

Transportation

I still don't have a car. I can walk most places or, as I did today to go to the dentist across town, summon an Uber. Two things need to happen before I buy a new car. One, they need to fix supply chain issues so I'm not paying more for the car than I did for the deck. And two, even though I can see just fine for now with glasses, I want to wait for after the cataract surgery. Which leads me to...

If Looks Could Kill

I have an appointment with the eye surgeon late in October. Unfortunately -- or fortunately, if you're as phobic as I am about shit touching your eyeballs -- it's not for the actual surgery, but for a pre-op consultation and verification that I indeed have cataracts. My vision continues to deteriorate, so it's a race to find out if I'll still be able to see a goddamn thing when they finally schedule the surgery. If I quit writing in here, it's because I lost the race.

Don't get old. It sucks. And it's expensive as fuck. One star, do not recommend. Yes, I know what the alternative is; my recommendation stands.

Le Français

On the plus side, I'm still doing French lessons every day. I have a hell of a streak going on Duolingo. One of my Uber drivers yesterday was from Paris. Fortunately, I didn't find this out until after the ride was over (he had an accent, but I didn't peg it as French at the time) and I went to tip him in the app. This is fortunate because I managed to avoid embarrassing myself by attempting to pronounce words in French in front of him, which surely would have resulted in him giving me a one-star rider rating, if not blackballing me from the app altogether.

I said I'm learning. I didn't say I was any good at it. Like I said, getting old sucks.

Movies

I know I haven't done a one-sentence movie review in a while. That's because I haven't been to the movies in a couple of weeks. That, in turn, is because nothing's appealed to me. This should change next month. Provided I can still see the screen.

Some of my blog entries next month, assuming I don't go blind first, will be for:

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

There's still space for other contestants, and I never win that one so don't be all like "I'm not entering a contest Waltz is in." What? You weren't all like that? Okay, cool. So enter.

You know what October means. Halloween shit everywhere. Creative October-themed WDC handles. Pumpkin spice everything. No more Green Day for another year, because September's done ended already. Christmas bullshit appearing in stores, if it hasn't already. Leaves falling off the damn trees for me to rake. And, of course, preparing for NaNoWriMo:

FORUM

October Novel Prep Challenge

(13+)
A month-long novel-planning challenge with prizes galore.
#1474311 by Brandiwyn🎶

You have until the 3rd to sign up, but why wait?

And some fun ongoing things that don't require you to get into an October mood:

FORUM

Question of the Day!

(18+)
Come answer a question, share a laugh, encourage one another, and bring me a coffee!
#2142667 by Lilli 🧿 ☕

No competition, no signup, just hop in and participate.

BOOK

Smile! (Groan?) You Know You Love These!

(13+)
Want to smile at least once a day? Then read these! Okay, maybe you'll groan some too...
#2177903 by Sum1's Home

What, I'm not funny enough for you? Add that blog to your favorites for a daily assault on your humerus.

There's plenty more going on here, of course, and I'm not trying to snub anyone by not plugging them right now. Feel free to add your own (or someone else's) in the comments below.

Tomorrow, it's back to the usual programming around here.

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