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 2 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 4 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.

August 8, 2021 at 12:04am

#1015284

Race to the Bottom

I'm not a person who seeks out instances of racism under every rug, but sometimes they smack you in the face.

4 Beloved Things ... That Have Surprisingly Bigoted Problems

Yes, it's another Cracked link. Such are the vagaries of the random number generator. That site's thing is countdown lists; one gets used to it.

4. Tattoos - People With Darker Skin Have To Deal With Shitty Artists

Everyone should have the right to make a terrible and permanent decision when they're newly 18 and deeply immersed in some fringe fandom or just after some really great sex. But for people whose skin tone resides in "can't find foundation at the drugstore" territory, it can be an annoyingly sensible process. If they just barrel into the tattoo shop, musculoskeletal guns blazing, it's entirely possible the artist on duty will explain to them that their options are severely limited, as colors lighter than their skin won't show up. Many refuse to work on them at all, including Ink Master season two winner Steve Tefft, who declared on camera, "I don't want the dark canvases. They take away half your skill set."

Or you could -- just spitballing here -- take the opportunity to improve your skill set. I don't have any tattoos for personal reasons (having none makes me unique), but an artist turning away people who want them because they can't be arsed to get creative with, you know, their artist job, just seems wrong.

3. Legalized Marijuana - Lots Of Green … For White Sellers

Entire articles could be (and have been) written on the intersection of racism and the prohibition of certain drugs, but now that weed is on the fast track to becoming the next booze (i.e., a perfectly legal pastime that just makes people really annoying), the shoe is on the other foot. And that foot is pretty well-heeled.

Most of the brewers I know are white, too. I'd be happy to see more diversity in either field, but you start to run into the usual racist problems: lack of general wealth, cops hassling darker-skinned people more (alluded to in the article) and so on. The lack of diversity in growers and brewers may be a symptom of this larger problem, not a stand-alone issue.

2. French Kissing - Was Just Regular Kissing Until American Prudes

Okay, so the French aren't exactly the most oppressed people in the West, but they're still the subject of scorn that honestly reflects a lot more on us than them. Take this whole "French kissing" thing. People have been licking each other in the mouth for thousands of years, but when European colonists showed up in North America, they weren't exactly sending their horniest. As a result, by the beginning of the 20th century, kissing with tongue had become so taboo that many people didn't even know it was a thing you could do.

Shh, don't tell them about "reverse cowboy."

American culture is, as you might tell by our dominant language, more derived from England than France, even though if it weren't for France we'd still be worshiping the Queen or whatever it is they do over there. And I don't know if this is true, but I heard that back in the early days of the Enlightenment, the French called syphilis the "English Pox," and the English called it the "French Pox." It sounds like something that should be true, anyway. We seem to have inherited the traditional English disdain for the French despite it being France that cozied up to us back when we were trying to stick it to the monarchy, after which they showed us what "sticking it to the monarchy" really meant.

1. Cryptocurrency - Another Reason It Sucks

When you picture a Bitcoin enthusiast, you're definitely thinking of a weirdly aggressive white guy, and there's a reason for that beyond their Elon Musk fan Twitters. Cryptocurrency has been dubbed "the currency of the alt-right" for reasons that no one understands but have something to do with it being decoupled from any government, and it's completely changed the economy of white supremacy, which is, ugh, yes, a thing.

I already hated Bitcoin and now I have even more reason to hate it.

Yes, two theater trips in one week. What can I say? I didn't have much to do yesterday, so I went to the drafthouse cinema.

One-Sentence Movie Review: Stillwater

This Matt Damon-led movie that you probably never heard of is surprisingly good -- what it lacks in plot advancement, it makes up for in acting, character development and scenery and I got through the slow parts by seeing if I could understand the spoken French without looking at the subtitles (it's set mostly in Marseille; the dialogue is mostly in English but I think the director wanted to demonstrate that the main character started out knowing maybe two words of French, so there are some French conversations and I understood about half of them).

Rating: 4/5

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