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 3, 2019 at 12:04am

#965446

Uncomfortable

PROMPT September 3rd

WDC is huge - there's no question about that. No matter how long we've been on the site, there is always more to learn. Today, I'm sending you on a mission with three easy steps:

1.) Go to the Community Newsfeed and comment on the post of a member you do not know.
https://www.writing.com/main/newsfeed/community
2.) Go to the Blog Board and comment on a blog you haven't read before.
https://www.writing.com/main/list_items/type/blogs
3.) Return to your own blog and share what you learned. In addition, answer this question:
How would a life where you regularly stepped outside your comfort zone be different than a life where you never did?

Okay.

1) I found a post by someone I've never met: "Note: HURRY....... HURRY...... HURRY...... A STORY,...". It featured:

Invalid Item

This item number is not valid.
#2198262 by Not Available.

Which struck me as a pretty awesome way to celebrate WDC's birthday week, and I said so. I've repeated the bitem link here to try to give it more attention.

2) This was harder, because I not only had to find someone I didn't "know," but also find an entry I felt qualified to comment on. (Hey, I just ended a sentence with a preposition again. Suck it, haterz.) I also wanted to avoid anything religiously or politically charged, because I'd end up getting sucked into drama, and I don't do drama.

What happened is I ended up at someone I *almost* commented on in Step 1 above; I thought this particular entry was thoughtful and, more importantly for me, focused on writing - not politics or religion. (I can't speak for the other entries in the blog.)

Dang if Charlie ~

didn't beat me to it, though - but I didn't see anything about avoiding stuff other participants have used, so nyah.

"Invalid Entry"

3) Some of what I learned is noted above. I also learned:

a) I need to get out more. I guess this is related to the "comfort zone" thing, but I've mostly only been checking out the work done by people who have reached out to me. I could do more reaching out, myself. Still, "comfort zone" issues or not, I'm not going to argue with someone's political or religious views. Not here.
b) Some peoples' minds are full of spiders. I'm not going to name names.
c) Man, there's a lot going on for Birthday Week. Enough to paralyze me with indecision if I let it.

As for the comfort zone question in the prompt, well... I do try to step out on a regular basis. That's what I try to do on road trips: combine the familiar (beer) with the unfamiliar (pretty much everything else). But there's more I want to do.

I might as well go ahead and admit it here: I'm trying to learn French. Part of the reason I don't go to other countries more often is that the potential language barrier makes me uncomfortable. Also, I can't say that I'm any good with languages - the only one I ever formally studied was Latin, and that was so long ago I took lessons from Cicero himself, and have forgotten almost everything about it except a few jokes. I also picked up some Hebrew at a young age, but, again... forgot. It's not like I could go to Israel and carry on a conversation.

All this... might as well call it what it is: fear. All this fear is mitigated if I'm traveling with someone else. At least then there's someone to talk to. But I can never find anyone to travel with me, so I'm stuck here. I don't mind traveling alone; in many ways, I prefer it. But if I'm sitting at a bar somewhere in Japan or wherever, I'd like to at least be able to have a conversation with the bartender, and since I'd rather be at places where tourists aren't, I can't rely on everyone knowing my own fucked-up language, however widespread it may be.

So, anyway, French. Yeah, I got it in my head some years ago that there are several places I want to visit. Two of them are Belgium and France itself. Another is Quebec (yes, I'm aware that French there isn't really the same, but at least I can count on more people being bilingual). Everyone in Belgium, I'm told, speaks about 40 different languages, but the big ones are French and Dutch. I could probably get by with English, but how cool would it be to know when someone's trying to say shit behind my back?

But what I want to do in France is tour the Loire Valley, because my favorite wine is a chenin blanc called Vouvray, which is only found in that region. It'll be bad enough once they find out I'm from the US, and I want to show an effort at learning the language.

So, we'll see if I stick with it. Supposedly, just the process of learning another language helps to keep one's mind flexible, and at my age, that's a real consideration.

In short, I don't want to stay in my comfort zone.

3 Like • Comment • View 7 comments

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