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 8 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 10 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.

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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').

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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 16, 2024 at 9:35am

#1062474

Dis Appointment

Rant time.

I had a doctor appointment scheduled for this morning. No big deal; regular check-up kind of thing. As you might be aware if you're reading this the day I post it, practically the entire country got sn*w dumped on it last night. My part of the country got off easy: maybe 2 inches, barely any on the roads. Not much, sure, but more than we've had for two years.

So naturally, things like schools, businesses, and non-critical clinics shut down or opened late. Okay, no big deal, right? Well, maybe. See, the clinic is part of a massive, bureaucratic, and very busy hospital system. They run pretty efficiently, but they have instituted some strict policies. Like, no-show for an appointment without something like 48 hours notice means getting charged in full; naturally, insurance doesn't cover that. It also means they drop you as a patient, because, like I said, they're very busy and don't have the patience for no-show patients.

You might think they'd be more lenient about such policies when we get sn*w, because everyone around here acts like they've never seen sn*w every time it sn*ws, but, like I said, bureaucracy, so no, I don't trust them to be lenient.

So, I woke up at the gods-forsaken cow-milking hour I'd have to wake up in order to account for sn*w-clearing and slower driving (the clinic is only 2 miles away, and I'm usually happy to walk it, but not on fresh sn*w in sub-freezing temperatures), and I checked their website, figuring, okay, if the clinic is closed, I'm off the hook.

It's not closed. It has a delayed opening at 10.

My appointment was for 9:30.

So there I am, bleary, blinking, no caffeine yet. What do I do? Show up at 10, figuring they're just going to try to cram everyone in? Show up at 9:30 anyway, because maybe the website was wrong? Go back to sleep, so they can potentially bone me hard? Call them? But they're closed.

Okay, I thought, maybe they have a phone system that auto-forwards in these rare instances. So, after double-checking all the websites I could think of, I got ready to try a phone call.

Which is when they called me.

That's good, right? Well, it would be, except that for some reason (possibly, but probably not, related to the sn*w), the voice on the other end was almost hopelessly garbled. She's probably trying to call a few dozen people this morning (like I said, huge hospital system), so she's understandably in a hurry.

Somehow, I manage to get the gist of what she's saying: reschedule for Friday morning at 10. Fine. I change my calendar accordingly.

It was only after the call ended that I thought to check the weather forecast for Thursday night and Friday morning.

Guess what. Go ahead. Guess.

7 Like • Comment • View 5 comments

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