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 5, 2019 at 1:18am

#965588

Feature (not a bug)

PROMPT September 5th

I spent some time today reading "Writing.Com 101"

(a normal Wednesday activity), and found a few entries describing some of the lesser-known features on WDC including the "Sliders Tab"

, "Macros"

, the "Ideanary"

, and "Portfolio Highlighting"

. In addition to these tools and features, there are 22 item types available for members to create, but only a handful make up the majority of content on the site. Take a look at the full list here: "Item Types and Their Uses"

Is there any item type available to you that you've never created? Any that you've never read? Any tool or feature on WDC that you haven't tried? Why not? What are the benefits of having these extra features available on a site dedicated to writing? (I have a feeling our restless muses are to blame, but I'd love to hear your thoughts!

)

The main pieces of software I used when I had a desk job were MS Excel and Word, and AutoCAD. I mention this here because, in a sense, Writing.Com can be considered software as well, and these four programs have something in common: they contain features that are used often, features that are used sometimes, and other features that are used only rarely.

When I first started using Excel, back when it was written for clay tablets and a cuneiform keyboard, I made it a point to learn everything I could about it - all the menu items, all the operators, all the built-in functions. There are many that I still use; plus, I've learned the programming language built into it, VBA. I'm not saying I'm any good at VBA but, if you don't mind a bit of braggadocio (where can I do that if not in my own blog), I'm damn good with Excel. Just ask Brandiwyn🎶

.

And yet, when I need some feature that I've hardly ever used, I need to consult the documentation. I have a vague memory of a programming rule covering this sort of thing, something like: 10% of the features are used 90% of the time, and vice-versa. Can't be arsed to look it up, but I think that captures the idea of it.

Point is, though, that long ago, I got the urge out of my system to exhaust a program's capabilities. My personal algorithm goes something like:

1) Identify the problem that needs solving
2) Assume that the program I'm using has a built-in solution to that problem
3) Find said solution.
3a) IF assumption turns out to be correct, THEN implement solution.
3b) ELSE defenestrate computing device.

Now here, I consider it part of my job description as Moderator to know what site features are available so I can help other members do step 3 above (can't help 'em with 3b, though). So I was aware of all the stuff in the prompt. But that doesn't mean I use all of it, just as I haven't written in every listed genre.

Still, someone else might make regular use of features I don't. The "Interactive" item type comes to mind. I find myself slogging through them occasionally as a moderator (you don't want to know, trust me), but if memory serves, I've never actually created an item of that type. Just never had good reason to. For some people, that's the only reason they come here, and that's fine, too (though I do know some good shrinks, if one of you is reading this).

I guess what I'm getting at is that while it's good to know what's available, I don't feel like I have to use every feature SM provides. So I don't.

3 Like • Comment • View 7 comments

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