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 11, 2019 at 12:04am

#965984

Idols

PROMPT September 11th

Today’s prompt comes from tah20! (With additions by me

)

Write about someone who truly moves/touches/inspires you. Do you know them personally, or admire them from afar? What do they do that makes them special?

Moves? Touches? Inspires? A Jedi craves not these things.

In considering this prompt, I racked my brains to come up with someone I knew. Each of my friends inspires me in his or her own way, but no single one really fits what I feel to be the spirit of the prompt. The closest fit is one I've mentioned before, the one I usually write for, who reads my stuff and is still my friend anyway. That's true friendship, right there - it would drive most people away.

So we're left with celebrities and the like: authors, directors, musicians, etc. - people I don't personally know but have had a great impact on my life.

I'm assuming, further, that I'm limited to living people here. Plenty of people who have died have shaped what I am and what I do. Leonard Cohen comes to mind, there; I first got into writing in a pathetic attempt to emulate his poetry. He was an established poet before he became a singer/songwriter/performer, and his songs reflect this background. He was one of the casualties of the dark year 2016.

That's the trouble with getting old. All your heroes start to die off and you're left holding the void. At least they've left a legacy.

I'm going to have to go with another singer/songwriter/performer, Bruce Springsteen. If you only know his work from the "hits," you're only seeing one facet of his talent, and you probably won't understand this. That's okay; it's a very personal thing with me, something I even hesitate to share here, in this context. But there's no escaping the history; from the moment I first heard Born to Run crackling from a shitty AM radio in a shitty Buick back in the 70s, I've been a fan.

It's not something I can readily explain, either. It's not like I fit into the categories of people he writes about. I tried to, long ago, but it's just not my life. There's a combination of things: the poetic lyrics, the music (which can as easily be droning and lost as it can be energetic and uplifting), the story - and there is a story, about someone who knew what he wanted and then reached out and took it, mostly on his own terms. I've never done that, myself, but I can admire it.

And wouldn't you know, I pick two people, one dead, one still with us, who are known to have achieved greatness in spite of - or, perhaps, because of? - crippling depression. That probably says something about me that I'd rather leave unexamined, for now.

This sort of thing is almost a one-way street, though. I can show my support by consuming their product, along with thousands or millions of other people, but I know I can never impact their lives, by myself, in the way they impacted mine. I'm not one for celebrity gossip, or hero-worship; they're just people, with the only difference between them and us being that they're well-known. And maybe a certain drive that I lack.

All this is not meant to diminish the impact on me of hundreds of other people - including my parents, who raised a stranger's child as their own. That takes a dedication that I certainly don't have. Yesterday was an anniversary of my father's birth, so I thought about what he was like at my age, when I was very young. I'm more like him than I care to admit, most of the time.

But he never did like Springsteen.

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