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 21 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 23 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.

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.

January 7, 2020 at 12:15am

#972848

The Story

PROMPT January 7th

What skill (craft, instrument, sport, art, etc) do you wish you could do but can’t? What’s stopping you from learning?

Writing.

Okay, no... all of them.

This prompt hits upon my greatest frustrations in life, so I'm going to try not to be melodramatic about it. I will probably fail.

As I've hinted in previous posts, I've always loved music. I've even learned theory and the basics of playing a few instruments. And yet... I can't.

I see art that people make, and it's like photos of another dimension: I can appreciate it, but I can never reach it myself. My attempts at drawing are pathetic.

I read books, watch movies and shows, and while I might have some skill as a writer, I seem to lack whatever creative spark it is that lets me be successful at it as anything but a hobby.

As much as I love beer, wine and spirits, even though I have some knowledge of their manufacture and the steps that go into making booze of all sorts, I can't participate as anything other than a consumer - not that I don't thoroughly enjoy that aspect.

Okay, so I don't care for sports at all, but I have no proficiency there, either.

We make allowances for all sorts of deficiencies in people, but there is one lack that we have no tolerance for, a lack that I have in abundance - and that is the absence of creativity.

Without that core, without that ability, I will always be an outsider.

It's not that I haven't tried to learn these things. It's that I'm empty inside, soulless, creatively destitute.

Okay, fine, so I lapsed into melodrama and self-pity after all. I'd been mulling all of this over for a couple of days, actually, after a couple of prompts ago inspired me to try to figure out exactly what makes me useless at music in particular, and art of any sort in general. I still haven't figured it out. I likely never will.

So I work on the one thing that requires the least amount of resources: writing. A pen and paper, or a keyboard and some computer chips - that's all it takes to practice. I do feel like I'm getting better at it, but there's still some aspects that elude me, that will probably forever elude me. To be able to express myself creatively, to be understood at some deep level (while still being all dark and mysterious and shit), well, that's a big part of what I wanted out of life. But I can't have it.

I generally try to focus on what I can do, and all of the good things I have. But sometimes all of that gets obscured by the void.

Story of my life.

All of these lines across my face
Tell you the story of who I am
So many stories of where I've been
And how I got to where I am
But these stories don't mean anything
When you've got no one to tell them to
It's true, I was made for you

6 Like • Comment • View 10 comments

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