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:

Write_Mikey_Write!

about 14 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 16 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.

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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