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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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

August 20, 2024 at 10:33am

#1075503

Some Clouds Are Just Clouds

This one's from Forbes, and to me is an exercise in suppressing my confirmation bias, because it's saying the same shit I've been saying, only by an actual mental health professional.

A Psychologist Explains ‘Oppressive Optimism’—And The Toxic Side Of Self-Care

Being a professional in a field doesn't mean you're always right; thinking that's the case would be another fallacy. Still, I think the article is worth contemplating. Whether my comments are is an open question.

Self-care has become a buzzword in wellness culture and for good reason—it’s essential for our mental, emotional and physical health.

Assertion without evidence can also be a problem.

These practices can work wonders, but when chasing positivity turns into an obsession—it can lead to what researchers call “toxic positivity.”

Which I've ragged on in here before, repeatedly... though not so much as to have exhausted my patience with the topic.

In essence, toxic positivity invalidates negative experiences by promoting the idea that one should always maintain a sunny outlook, regardless of circumstances.

I believe I've used examples of that before like "My dog died." "That's great! Now you can get a new puppy!"

Here are three specific examples of how self-care can slip into toxic positivity and end up doing more harm than good.

As this is not Cracked, the list actually counts up.

1. The Social Media Mantra—“Good Vibes Only”

While surrounding oneself with positivity can be uplifting, the insistence on “good vibes only” creates an environment where negative emotions are not just unwelcome but are seen as personal failings.

I'm not sure this is so much an insistence on toxic positivity as a desire to not get your own vibes harshed. Like, you're at a party, and everyone's having a great time, and one of your friends staggers in late and bleeding. "Got in a wreck," she moans. Normally, you'd probably be there for your friend, call an ambulance for her, maybe even wait in the ER with her. But you're at a party. How dare someone turn it into an emergency!

2. Oppressive Optimism—“Everything Happens For A Reason”

I've railed against that duck-billed platitude before, and I'll do it again.

Optimism is crucial when coping with negativity...

Another assertion without evidence.

...but the belief that everything happens for a reason can invalidate genuine feelings of fear and uncertainty.

This is related to "it's all part of God's plan," though that one's more specific to certain religious people.

3. Affirmation Overload—“I Am Strong, I Can Handle Anything”

Picture someone going through a tough divorce, constantly telling themselves, “I am strong” and “I can handle anything” to keep up their confidence and stay positive. While this might seem helpful, it might stop them from sharing their pain and struggles with loved ones, out of fear that admitting vulnerability will make them look weak or uncertain about their decision.

And maybe that no one wants to be around them if they're not going to give off good vibes.

There's not much more to the article, really; the conclusion boils down to "seek help," which is fine advice, but what I'd need help with would be finding a shrink. Too much work. I'll just stay over here and be grumpy by myself.

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