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 11 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 13 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.

March 28, 2022 at 12:01am

#1029594

Just Breathe

I'd heard about these fools way back in the 1980s.

The strange, sad Bay Area ‘diet cult’ that fell apart over a chicken pot pie

For most dieters, his shopping list on that fateful day in 1983 (chicken pot pie, chili and biscuits) would be, at worst, an embarrassment. But Brooks was no average weight-watcher. He was the founder of the spiritual and pseudoscientific movement known as Breatharianism, famous for spreading the gospel that humans could live on air alone.

They can. Just not for very long.

He claimed he hadn’t eaten in 19 years. To his followers, the binge was an unforgivable sin — as if God himself had taken a bite out of the forbidden apple.

Some people simply believe what they want to believe, all evidence to the contrary notwithstanding. Breatharianism wasn't even the worst example.

Yet that very public scandal didn’t stop Breatharianism. Instead of dying out, the movement spread around the globe, fracturing over the decades into stranger, more dangerous forms. It’s even helped shape health and wellness culture as we know it today.

And sometimes, evidence to the contrary, against all rational expectations, actually strengthens one's beliefs.

“Breatharianism is a philosophy that believes that the human body, when it’s in perfect harmony with itself and nature, is a perfect Breatharian — you know, all the constituents that we need is taken from the air we breathe,” Brooks told Snyder, in front of a studio audience that seemed both amused and entranced by his words.

And this leads to what is perhaps the most insidious conclusion: that if you fail in whatever you're doing (in this case, fasting), then the problem is you not being pure, resolute, or spiritual enough. This can easily spiral into dangerous territory... and it even happens in more mainstream religions.

He went on to make other strange, spurious claims, including that Breatharian mothers don’t need to feed their babies, who are born able to survive on air and sun. He also said that hunger strikers who die are killed by their death wish, not from starvation.

Part of me doesn't care what happens to people who fall for this shit, but the baby shouldn't suffer for its mother's idiocy.

His logic shifted again in 1993, when he told the Seattle Times that he no longer believed food was an addiction. Though he still believed food was a poison, he also believed it could serve as “medicine,” a salve for low-quality city air. He himself occasionally balanced his aura with orange juice, honey and Twinkies, he said.

Breakfast of Champions.

In 2009, the official gospel of Breatharianism was updated again, this time with a convoluted explanation of how a McDonald’s cheeseburger meal and a Diet Coke can help keep a Breatharian healthy. In a fifth-dimensional universe, apparently, the “base frequency” of the meal aligns with the needs of man.

You gotta wonder if the company paid him for the advertising. Hell, if I were him -- assuming I could live with myself after fooling all those gullible people -- I'd be taking bids from food manufacturers. Highest bid gets the "best vibrational energy" spiel for that week.

Even though Brooks was widely ridiculed in the media, it’s easy to see why his ideas found a foothold in the ’80s and ’90s. Low-fat and low-calorie junk foods like Lean Cuisine and Diet Coke filled Americans’ fridges and minds, turning food into a deep source of shame. The idea of self-restriction as the essence of health and beauty was shamelessly promoted in books and daytime television.

"If you're sick it's YOUR FAULT. You're doing something wrong. Stay neurotic. Keep buying our fix!"

Wellness culture, like Brooks, tells us to fear aging and detest weight gain, as if these things are moral failures rather than an inescapable part of the human condition. Whether through nutritional deprivation or immortality-through-technology, transcending the body and its flaws is all the rage right now. And what comes after humanity but holiness?

The only moral failure involved here is in believing the bullshit.

Now if you'll excuse me, I have a box of Twinkies to inhale.

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