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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Show Recent Comments

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

October 2, 2023 at 8:53am

#1056555

Bad Influence

I've been banned as a bad influence, so I can identify with this Cracked article.

5 Innocent Things Banned as Bad Influences

I, too, was innocent.

What do you do when your citizens come upon something new? You must ban it, obviously. New things lead to new thoughts, which lead to new actions, which lead to your downfall.

Probably why it took fire so long to really catch on.

5. Syria Banned Yo-Yos, Thinking They Caused Drought

Every once in a while you hear about some country getting all panicked over a superstitious belief. Then you remember that, here, people still think floods are caused by God being angry that we let gays exist.

Looking for something to blame, the country’s holy men turned to a new toy people were playing with: yo-yos. Everyone was praying to the heavens above for rain, they reasoned, and meanwhile here were yo-yos springing to the ground below, and that surely disturbed everything.

Ha ha those idiots. Don't they know yo-yos could have been used to dowse for water?

At the time of this ban, international reports had to explain to people just what the toy was. It was an invention commonly known as the bandalore, according to dictionaries at the time, and had been called a “quiz” in England.

Which would make yo-yo tricksters bandalorians.

You may be tempted to laugh at the confused holy men. But shortly after the ban went into effect, the rains returned, so the holy men got the last laugh.

And this, folks, is exactly why we need to avoid confusing correlation with causation, or to think that because you took skunk oil and your cold symptoms lessened, it was the skunk oil that lessened your cold symptoms.

4. Germany Banned the Game ‘Risk,’ Saying It Would Induce Feelings of Militarism

That would be like the US banning Monopoly because it would induce feelings of capitalism.

3. The BBC Banned Desk Lamps

Writers with lamps would pen “smut” and “innuendo,” warned the book, inspired by the light into producing “furtive” and “degenerative” programs.

Hm... *searches Amazon for desk lamps*

2. China Banned Videos of Eating Bananas

Speaking of smut and innuendo.

In time, we came upon further banana videos that — while not porn, by any conventional definition — were so erotic that we refuse to embed them here.

I'm sure we can find them ourselves.

1. A Town Banned All Concerts When a Neighboring Lot ‘Accidentally’ Booked Rage Against the Machine

If the band performed as planned, people might be able to hear the lyrics all the way in town, residents complained, which would inspire in them all kinds of corrupt thoughts. Or maybe the thousands of concertgoers would descend upon the town and riot.

Worse, someone might... dance. Quelle horreur! After all, you know why Baptist teens aren't allowed to have sex? Because it might lead to dancing.

(Yes, I know the incident in question took place in Utah, better known for LDS than Baptists, but it's a joke.)

3 Like • Comment • View 1 comment

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