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 6 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 8 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.

August 25, 2020 at 12:06am

#991528

Wave Function Collapse

Not a lot of commentary today. I started late and I want to hurry up and get to the drinking part of my evening.

But Contest results below!

http://nautil.us/issue/83/intelligence/how-to-make-sense-of-quantum-physics

How to Make Sense of Quantum Physics
Superdeterminism, a long-abandoned idea, may help us overcome the current crisis in physics.

Mostly I'm just leaving this here because it touches on a lot of subjects I tend to post on, and it starts out as a pretty good explanation of quantum physics. It goes on to branch out into philosophy and even questions of free will. Recommended reading -- just remember the entire second part is speculation.

So on with the marketing question from yesterday.

Mini-Contest Results!

Great entries, and tough to pick just one -- but I managed. As usual, everyone will get another chance in a few days.

NaNoNette

, the phrases "tone-deaf," "bad optics," and "read the damn room" come to mind there.

Sumojo

, this is exactly why I try to stay away from hot-button issues. I don't always succeed.

⭐Princette♥PengthuluWrites

, how that got past the number of people who would have had to have been involved is a mystery. Perhaps they were all drunk.

prettypoetry, yeah, I remember that. You do one thing and you've been doing it for decades, and all of a sudden you want to change the formula that works (that is, without seismic macroeconomic shifts as with JC Penny and Sears, see below)? See also: New Coke.

Wordsmitty ✍️

, what in the hell were they thinking?

Lostwordsmith

, true, not really what I was looking for, but darkly hilarious.

Charity Marie - <3

, I could say the same thing about Sears. Sears built its entire brand by people in remote areas being able to order stuff from them through the mail, from a catalog. They were huge; at one point, they had their name on the tallest building in the world, and they were a household name. The Internet comes along, and Sears sticks to its b&m model; Amazon adopts an updated Sears strategy and becomes a juggernaut. Sears gets gutted by private equity and turns to vapor. As for Sherwin Williams, true story (at least as far as my memory might be reliable): the first time I saw an SW logo as a kid -- it hasn't changed in at least 50 years afaik -- I remember thinking, "but where is the gravity coming from that's letting the paint drip off the planet? Point being, I was a huge nerd even as a child.

Everyone who commented without an example, I appreciated your responses too -- thanks!

In awarding the winner, I wanted to consider something as close as possible to the Tropicana and Coke fails, and the idea of a marketing strategy being so outrageously bad that it led to the company becoming not-a-company, so:

Wordsmitty ✍️ gets the Merit Badge for: Just For Feet, a giant shoe retailer, decided to take the plunge with a Super Bowl ad to an estimated 120 Million plus viewers on January 31, 1999. Unfortunately, ...

The commercial began with four caucasian-looking men in a Humvee with the license plate "Just For Feet." They track footprints in Kenya until they overtake a black man and offer him water. He collapses (drugged?) and they put a pair of Nikes on him. When he wakes and sees the shoes, he screams "Nooooooo!" and runs off trying to shake the shoes from his feet.

Quoting the book, "The backlash from the ad was immediate and fierce." The company didn't survive to see the new century.

Thanks again and we'll do this again soon!

4 Like • Comment • View 1 comment

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