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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Show Recent Comments

10 Most Recent Blog Comments:

Elycia Lee ☮

about 3 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 16 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 19 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 21 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

April 17, 2020 at 12:08am

#981295

Home Alone

Hey look. Another article about being quarantined.

https://www.technologyreview.com/2020/04/02/998440/lockdown-was-supposed-to-be-a...

I love how the header image makes sure the Apple logo on the notebook computer is in focus while everything else is out of focus. If Apple didn't pay them for that, the website is doing it wrong.

Lockdown was supposed to be an introvert’s paradise. It’s not.
Calendars cleared by coronavirus are filling up with virtual happy hours, and some people are starting to feel exhausted.

Really? Because I'm not seeing that happen.

This was supposed to be the moment for introverts—the disaster preppers of our new, covid-ravaged social lives. Those who cherished their time alone at home were already experts at voluntary self-isolation.

And you know what? It is our moment. My whole life has been leading to this.

But as people began to adjust to isolation, they started to find ways to bring their outside social lives into their homes.

My outside social life, apart from drinking at bars, involves typing to people on the internet. No one invites me to anything else. Well, rarely. Mostly just in December. You think the bitching level is high now? Imagine if this shit had started in November.

Calendars that had been cleared by social distancing suddenly refilled as friends, family, and acquaintances made plans to sip “quarantinis” at Zoom happy hours, hold Netflix viewing parties, or just catch up over Google hangouts.

Hey, look, three stock recommendations. Four if you count the Apple ad at the top.

“There’s no way you can pass that off as having other plans,” says Jaya Saxena, a staff writer at Eater, who is currently socially distancing with her spouse in her apartment in Queens, New York. “The only excuse is ‘I don’t want to,’ and no one wants to hear that right now.”

"I don't want to." There. That was easy, wasn't it? Or you can always fake a scratchy throat. Just be sure to assure them it's not the 'rona.

The reality is that introverts don’t want to be alone all the time, and extroverts can appreciate moments of quiet. But the division exists as a way to describe how people gather their energy: introverts charge up by having quiet time to process, and extroverts do it by socializing.

That's still very simplistic. Look, I'm not antisocial or misanthropic. I like meeting people. I like hanging out with people. I just can only take so much of it before I have to go do something solitary. This applies online, too; I don't like multiplayer video games.

For some, staying home means solitude and a lot of extra time. Others are trying to finish school, homeschool children, or work under difficult conditions. As one group looks for things to do, the other longs for a free moment to leave the home and hunt for toilet paper.

Not only have I been preparing my entire life for this, but I'm in an extraordinarily fortunate position in that I have no other obligations, and I don't need to leave the house; I have groceries delivered, and I order other necessaries online. I still haven't found a source for toilet paper, but I haven't been looking very hard because I'd just bought a good supply before people started to decide that it was Official Currency of the Apocalypse.

Introverts socially distancing with others might feel an additional layer of stress, even before the first virtual happy hour invitation, Rutledge notes. “Staying at home with others places a burden on introverts because they are not wired for full-time interaction,” she wrote in an email.

I do have a housemate, and she's also home all the time. Fortunately, it's a big enough house, and we generally occupy different areas of it.

Stacy, who works for an ed-tech company near Albany, knows how that feels. She used to meet friends a few times a week to play Dungeons & Dragons. (Like Tarek, Stacy asked to be identified by her first name only.) Now, those physical games have moved online, through the same laptop camera that provides a portal to all her work meetings.

I played D&D with a group online for a couple of years. We're supposed to start up again, but I haven't heard back from the group. But yeah, there are tools out there for doing the standard D&D experience online. It has its advantages. I don't suggest playing D&D on your work computer, though. Unless you're the boss.

So yeah, I feel like I'm handling this better than most. I'm trying not to be smug about it, because the last thing I need is to alienate even more people. I might want to hang out with them again if this ends before I croak.

3 Like • Comment • View 3 comments

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