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!

2 minutes 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.

Adherennium Plotting something

about 2 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.

May 8, 2024 at 10:33am

#1070719

Be Positive

One reason conspiracy "theories" flourish is that, sometimes, an actual conspiracy is brought to light. While today's article, from MPR, doesn't quite rise to the level of major international conspiracy, it's enough to make you wonder what other similar things are going on.

Online dietitians backed by General Mills, big food companies using ‘anti-diet’ language to promote junk food

This is like finding out that PETA, the pseudo-animal-rights organization whose idiotic performance art ensured that I will never become a vegetarian, is actually funded by KFC. And yet, this is both hilarious and entirely predictable.

Cupcakes. Frozen Pizza. Ice Cream. Cereal. These are some of the sugary foods that a slew of social media influencers are encouraging folks to enjoy guilt free.

Honestly, I'm not opposed to that message. One reason we're so damn neurotic as a society is that lots of us have been convinced to feel guilty about everything pleasurable, instead of simply enjoying it. It's Puritanism all over again, and I won't put up with it.

But I say these things without any benefit other than my own enjoyment at turning out to be right. Certainly, no one's paying me. Not even attention.

However, a joint Washington Post and The Examination investigation found that major food companies, including Minnesota-based food giant General Mills, are reportedly capitalizing on the campaign by paying online dietitians to get people to consume more of their highly processed foods.

Calling the people involved "online dieticians" is questionable, at best. Having watched a couple of videos about diet advice doesn't make you a dietician, but that, combined with a helping of chutzpah and earnest confidence and maybe a nice paycheck from Little Debbie, can convince people that you are. It's like how people spread the misinformation about ivermectin and Covid.

Recently, General Mills, one of the biggest food companies in America, has started adopting the anti-diet philosophy as a way to promote their products. So, they’re doing this through a multi-pronged campaign that involves funding influencers online to promote this message, funding research and also hiring lobbyists to fight back against federal regulation.

Just to be clear: I think that all of these things are acceptable in a society that values freedom of speech and association. What's not acceptable is lying about it, or failing to disclose it.

We reached out to General Mills, and they say that they comply with federal regulations, and are working closely with scientific health nutrition experts to make sure that the information that they’re putting out there is accurate and based in evidence.

I can hear its nose growing from all the way over here.

I think it’s best to, when we’re approaching social media, to have a skeptical mindset. And, probably I would recommend people turn to their doctors for advice, as opposed to influencers online.

And sure, doctors are human too, and susceptible to outside influence. The shady practices of pharmaceutical companies are one way they can be led astray. So they're not always right. But they're far more likely to have the knowledge and experience to consult on things like this than some rando on the internet (myself included).

Skepticism (that's scepticism if you're British) is a good thing. Better that than naîve acceptance of everything you see online (or in ads or wherever). But that includes skepticism of conspiracy theories. Or conspiracy-adjacent theories.

7 Like • Comment • View 2 comments

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