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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 3, 2021 at 12:01am

#1020692

Tourist Trap

I get the impression that today's prompt is meant to inspire fiction. I'm certainly not above writing fiction, but this hits a little too close to home.

PROMPT November 3^rd

You live in a tourist town. There's always an 'interesting' mix of visitors. But this year they are especially... different. In what way?

A few years ago, my city decided to remove one of the Confederate participation trophies that stood in a prominent location, taunting, among others, descendants of the people freed after the Civil War. This decision pissed off all the right people (pun intended), who descended upon my town from other parts of the country (including, amusingly, the North) and protested.

If it had stayed in the realm of protest, fine. One major founding principle of the US, promoted by someone who lived just outside of town at the time, is the guarantee of freedom of speech. I'm a fan. As much as I disagree with the ideologies of the protestors, they have the right to express their opinions and, in fact, I want them to speak up so I know who to avoid.

But of course, it got violent, several people were injured, and three died.

I'm sure you heard about the event, even if you're not in the US. It made my town a household word the world over, a representation of the beginnings of the New Civil War: Charlottesville.

What doesn't get mentioned enough is that almost everyone involved in being a racist asshole back then was from out of town. Tourists.

Thing is, I'm usually inclined to consider all sides (there are always more than just two) of any issue, but in this case, one side wants people to try to get along, while another side would like to see me and others dead or, at the very least, marginalized..

Oh, sure, I can pass as one of them, but if they got to know me, they would know I am the Enemy. "Jews will not replace us," they chanted, tiki torches held high as they marched on the grounds of UVA. Then they have the chutzpah to accuse me of intolerance for condemning them for racism.

That kind of rhetoric is alarming, but how much more dread was felt, every freaking day, by descendants of slaves walking by a statue honoring Robert E. Lee? "You don't matter," said the statue, its lips resolutely mute. "I worked in life to own your ancestors, and behold, people put me on a pedestal." It'd be like putting up a heroic statue of Heinrich Himmler.

The carpetbaggers called for the preservation of the statue in its prominent location, saying, among other things, that to remove it is to erase history. Erase history? Hardly. History is still in books -- oh, wait, I forgot, a lot of them don't bother to read. Okay, it's still in videos online. If anything, removing it is one step in erasing the worship of the losers on the wrong side of history.

I live in a country that's weirdly prudish. All it usually takes is one complaint, if it's from the right person, and a book is banned, a statue is draped to cover its stony genitals, or an art exhibit is closed because a child might see a *gasp* female nipple. But if you have a problem with seeing a statue of someone who fought for the ability of people of one race to own people of another race? Oh, suck it up, that was in the past.

And the war was indeed about slavery. Oh, I've heard the bullshit about "it was over states' rights." Yeah, states' rights to enable slavery.

Four years after the protests, war drums still echo.

This year, the statue finally came down, quietly and without further bloodshed. I have no idea what happened to it, and honestly, I don't give a shit. Someone posted a meme of a picture of it getting hauled away, with the caption: "Virgil, quick come see, there goes Robert E. Lee."

If you don't get the reference, look it up. I'm not in the mood to post music right now.

So yeah, come see lovely Charlottesville sometime. We like an interesting mix of visitors. Just leave your bigotry at home.

11 Like • Comment • View 12 comments

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