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:

Elycia Lee ☮

about 5 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 21 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 23 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

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 Elisa: Middle Aged Stik

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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