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!

a day 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

a day 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 30, 2019 at 12:55am

#966998

Wake Me Up When... Wait, NOW?

PROMPT September 30th

On this final day on the competition, reflect on the month. What was your favorite prompt, and which challenged you the most? Any highlights from your offline life? What are you looking forward to in October?

I'm used to the months flying by, these days, but this month sped even faster than usual. I must be older than I thought.

I'd have to say the "special place" prompt was my favorite, because I got to talk about my favorite thing: drinking. Reading others' responses was fun, too, but I especially enjoyed being able to relate a recent experience of my own, there. "Pappy? Happy!"

Challenging? Probably the one about sports ("Athletic Non-Supporter"

), for the polar opposite reason: having to talk about one of my least favorite things. But hey, that's what I'm here for - stretching my topics. Honestly, I've enjoyed the prompts this month, maybe because it wasn't the standard weekly format. There weren't any that really felt like a chore.

Offline life? What's that? I haven't had one of those in decades. The closest I came was going to the conference in DC, but that was sponsored by a website I've been frequenting for even longer than I've been on Writing.Com - so no, the only part of it that was "offline" was the drinking, and even there, I have a social-media-for-drunks app that I use to record my alcoholic experiences.

And you know what? This is a good thing. The internet is the greatest advancement in human communication since movable type. Sure, it has its problems - doesn't everything? - but we have access to a body of literature and entertainment far more comprehensive than that of the famed, lost Library at Alexandria.

I'm always hearing people saying stuff like "I'm going out into the wilderness. No internet for a week! Hooray!" I don't know which is worse - the idea of being in the wilderness, or the idea of being without internet for a week. Like we should be feeling, I dunno, guilty or something about being connected to the entire fucking world.

Leave it to humans to create a vast, interconnected civilization to live, work and play in, and then get tired of it and go sleep on a damned rock.

Now, I understand that some people enjoy camping and whatnot. I even understand why. And I'm not being judgmental - hope they enjoy the experience. I'm just saying: uh-uh, not me.

...that said, I did spend a week on a mountaintop in Colorado last June, and didn't open my laptop even once, but again - not something I'd ever have had the opportunity to do if it weren't for meeting people on the internet. (To be clear, though, I was in a heated cabin with electricity, and I dined on fine food and drank wonderful beer. I have my limits.)

So. October. This is where I plug my friend's activity:

FORUM

October Novel Prep Challenge

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

Because I'm a terrible person, I may not participate, myself. I'm out of novel ideas, and I have like four of them written and in desperate need of editing. Every time I start, though, I get frustrated and I go play video games or binge-watch Supernatural.

Still, I'm involved in running the activity, so come play along.

Another reason I'm being lame about it is that I'm way behind on my contest entry goal for the year, and I need to play catch-up. So that's a goal for October: play catch-up on the writing I've fallen behind on.

I've been at the French lessons for a month, and plan to continue that through October, also - even though I've already learned how to order "une bière." Deux bières, even. I mean, if that's the only French I ever remember, that's okay.

Not to mention the weight loss / exercise thing - over nine months, now, and while progress is slowing down, it's still... you know... progressing. Though the craving for a pepperoni pizza is starting to overwhelm me. One of these days, I will fail at the regimen. Today, however, is not that day.

If you're here from 30DBC, I hope you'll stick around - because I'm not planning to stop writing in here. Might not be every day, but I still have plenty to say. Either way, thanks for reading!

1 Like • Comment

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