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 16 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 18 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 12, 2020 at 3:20am

#977844

Individuals

Today's entry is #3 of 8 for:

Journalistic Intentions

[18+]
This is for the journal keeping types that come to PLAY! New round starts July 1!
by Turkey DrumStik

Women and Autism. Towards a Better Understanding | Sarai Pahla | TEDxMünster

I didn't pick this video from the prompt list for any particular reason; like the other entries I do, it came up at random.

A brief summary for anyone who's bothering to read this but can't be arsed to watch the video: a large, autistic black woman describes her struggles and frustrations in the dating world.

On Diversity

I said "large, autistic black woman" above. These terms are loaded and I can get in trouble for using them, but they're reflective of how the speaker defines herself. The whole talk is about how she has trouble finding love, but in the last 20 years she's been on more dates than I have, so my sympathy is limited.

That's because my last date was 20 years ago. That's about when I met my future ex-wife, and since then, I, supposedly a mid-sized neurotypical white man, haven't had the motive or opportunity. The Venn diagram of "people I might want to date" and "people who might want to date me" has no overlap at all.

I say "supposedly" there because whenever I see writing or speech from someone on the spectrum, there's almost always some aspect where I can go, "Oh, yeah, I can relate to that." Yes, even this chick.

That's because, regardless of looks, diagnoses, race and gender, we're all human, and thus we have more in common than we have differences. I find it unfortunate that other people don't see it that way, but there's not much I can do about that.

Now, I don't watch a lot of TEDs. They're just not all that compelling to me, in general. Someone sends me one, I'll watch it, but it's not a regular thing. But this is the first one I've seen where they cut to the audience during the talk. And I don't know why. The audience is generally unreactive, like maybe they've been coached on keeping an autistic speaker comfortable.

On Conformity

So, we humans have more in common that we have differences, I said above. But sometimes the differences stand out like a giant at a dwarf convention. This speaker highlights her own differences in discussing her struggles to find companionship, and relates them to her autism.

I can sympathize to an extent. I'm not autistic, or at least I haven't been diagnosed, but I am weird. There's nothing I can do about that. If I try to hide it, I'm not being "authentic." If I don't, people shun me. Maybe if I got a doctor to certify that I'm on the spectrum, people would be more understanding of my idiosyncrasies. "He does that because he's autistic" generates more compassion than "he does that because he's weird."

On the other hand, nothing has been more liberating for me than not having to conform to society's ideas of what I should be like.

On Social Signals

Spectrum or not, I don't get social signals.

The speaker here talks about an ideal date: they're in the same room, but they're texting each other.

Much has been written about the downside of internet and remote connection. Writers bemoan the lack of face-to-face interaction, and say things like "you miss stuff if you're just texting." So I think a lot of people would find this strange.

I don't understand that. I have trouble understanding what people are saying, especially if there's other noise in the room. But with a text, or an email, or an IM? I know exactly what they're saying. It's logical to me. So what she's talking about? I get it.

So, like I said - spectrum or not, we're all human. All different. All alike.

3 Like • Comment

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