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.

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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.

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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.

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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.

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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').

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
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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

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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.

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June 7, 2023 at 11:59am

#1050744

Choice Responses

"None of your business" is always an acceptable response to a nosy question.

So you don't want kids. Here's how to respond to unwanted comments

A growing share of childless adults in the U.S. don't expect to ever have children, according to a 2021 Pew Research Center survey. Some people gave specific reasons, like medical conditions or finances, but a lot of people said they just don't want to.

And yet, almost no one ever asks "Why do/did you want children?"

No one needs to give a reason for their life choices. If pressed, "I just (don't) want to" should more than suffice.

If that's you, you might find yourself facing unwanted commentary or questions. Angela L. Harris can relate. She's child-free by choice, and she says people often question her choice or want to know all the details.

What details? Kids are messy and chaotic and smelly, and a net drain on resources? Those are the details that matter.

She says, first of all, to remember that you don't owe anyone an explanation: "If you don't feel like explaining, don't explain. Your life is your life."

See? Even the psychologist agrees with me.

Sometimes Harris' responses might be more sincere; other times, she opts for levity. "I think there's a playful and joking way in which you can respond," she says.

Thing is, having kids, or not, is the actual definition of a major life choice. And yet, you don't get a lot of "Why did you buy that house?" or "Why didn't you choose a hybrid car?" with some slightly less major life choices. Any of those choices usually involve not just one, but a myriad of reasons, and sometimes entire pros and cons lists. There's rarely, if ever, just one reason why someone does something. I know I don't even get out of bed unless I can think of at least two reasons why I should.

The article then presents a few of the questions, and her answers, in graphic meme form because that's the only way to get attention these days, except for short-attention-span vertical videos.

Format notwithstanding, they're all good answers, even if they do present the questioners in a rather unflattering manner. Even nosy people are often well-meaning, and I'm inclined to give them the benefit of the doubt until proven otherwise.

Harris acknowledges that having this conversation with your parents or your partner can be difficult. She stresses waiting until you feel ready to have the discussion.

Okay, sure, parents, I understand. But it seems to me that having this discussion with a potential partner as early as possible would be a good way to avoid wasting the time and energy of everyone involved. Back when I was still dating, I tried to determine pretty quickly if she had baby-rabies, and broke it off before either of us got involved in something we didn't want.

If one partner wants seven kids and the other wants two, perhaps a compromise can be reached. But if one absolutely wants kids and the other definitely does not, well, there's no compromise there (unless you're one of those assholes who abandon your family).

Your Turn: If you're child-free by choice, we'd love to hear how you respond to unsolicited questions and comments.

Well, I won't be commenting to NPR, but that's one of the many reasons I have a blog.

"Don't you want a little Waltz running around?" Oh, hell, no; I remember what I was like as a kid.

"If you wait until you can afford them, you never will." And?

"Who will take care of you when you're old?" Bringing another life into a dying world just so you can have free nursing later in life is the absolute pinnacle of selfishness.

"What do you have against children?" Nothing (usually). As with dogs, I think they're just fine; I just don't want to own one.

"Why don't you want kids?" Why do you?

"When are you going to have kids?" When there's a shortage.

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