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 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 25, 2022 at 12:02am

#1031312

Branding

The penultimate entry into this round of "Journalistic Intentions"

[18+]:

Bobcats are fighting pythons

Actually, I just like saying "penultimate." Kid Me took a while to figure that one out, because it was before the internet and I never could be arsed to open a dictionary for a word that gets used so rarely. So for a long time I thought it was a synonym of "ultimate," like how "inflammable" means the same thing as "flammable."

Speaking of English weirdness, the sentence up there is ambiguous again. Are bobcats really pythons who are fighting? That would certainly be surreal. I like it. Let's go with that. Oh, wait, no, I guess the bobcats are fighting against pythons.

Pretty sure there are a few high school sportsball teams called the Bobcats. Are any called the Pythons? Probably. There are a lot of high schools in the US, and sometimes you have to get creative with the names. I went to two high schools, in succession. I didn't move; a new school got built and I was in its district. We all got to vote on the name of the new school. Now, what you need to know is that the mascot of the elementary school I attended, which didn't have organized sports (and they never let me play the disorganized ones because I was a nerd), was the Little Indians. You'll see why in a second. The middle school was the Spartans, for some utterly obscure reason. And the first high school was the Indians (which of course explains the elementary school mascot). So, two years into high school, and I never got to be at a school whose spirit animal was... well... an animal.

I should point out right now that yes, of course these days we understand that a lot of "Indian" type mascots are horribly racist. However. The high school's nickname was chosen in acknowledgement of the local tribe. As soon as people started seriously questioning things like "Redskins," naturally (and appropriately), they started to question that one as well. So they did the right thing and actually asked the tribe, many of whom had gone to that high school.

Basically, the tribe said, "We like the name, but lose the feathered headdress. That's not even historically accurate." So they changed the logo but kept the name.

Anyway. As I was saying, after two years as an Indian (the mascot, not the heritage), they went to choose a name for the new high school and had us vote on it. Whether our votes were fairly counted is a question we will never know the answer to, but at least they pretended to give us input into what the school would be branded as. This being before the Internet, no one suggested "Schooly McSchoolFace." But, as it was 1981 and all the cool kids were reading X-Men comics when we weren't fanning ourselves over Star Wars, we (supposedly; I'm still not convinced the vote was fair) collectively decided on the Wolverines.

So even though I finally went to school with a nominally animal mascot, I knew, deep inside, along with all the other kids who voted for that name, that it was actually named after a fictional Canadian mutant antihero whose only connection to anything in the area was... well... nothing.

Hey, while we're on the subject of mascots, there's a professional sportsball team nominally out of New York called the Jets. They're actually based in New Jersey, though, which is yet another example of how New Jersey gets fucked out of the spotlight in favor of a few islands to its northeast. But I digress. Would it really be too much to ask that another NFL team change its name (the team formerly known as the Redskins had the chance, but blew it) to the Sharks?

I mean, come on. That would be awesome. You know that would be awesome; admit it. Jets. Versus. Sharks.

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