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 9 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 11 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.

June 1, 2021 at 12:02am

#1011075

Kids These Days

Welcome to June. My inner optimist says it'll be different than May; my inner pessimist fears that he's right.

Let's start this month with an entry for "Journalistic Intentions"

[18+]. There's still time to join in the fun there if you want.

CHOP Kids First

My state, Virginia, is often cited as having the largest percentage of vanity license plates in the US.

Honestly, I don't care one way or the other. Some of them can be amusing. Others have indecipherable meanings. But real creativity can come in when one combines vanity plates with special commemorative plates. And Virginia has a lot of them, too.

For example, my optometrist, who went to UVA, got UVA tags. These consist of a giant orange V logo on the left side, which gave her the opportunity to add ISION as her personalized tag, so when read in full, it says VISION. Cute. On brand. Glad to have someone that creative taking care of my eyeballs. On the other end, I hope whoever got AGINA

on one of those is a gynecologist.

Other commemorative plates are more controversial. Every time I see the one based on the Gadsden flag

(99% of the time, these are on oversized pickup trucks), I assume the driver is a raging asshole and give him (99% of the time it's a "him") a wide berth and a short "thank you" for advertising his assholery. That's what I like about freedom of speech; it lets me know who it would be a waste of time and energy to listen to. "Dont Tread On Me" is translated, by me at least, as "Tread on THEM," where "them" is any sort of minority.

Another problem one is the "Choose life" logo. Okay, it wouldn't be problematic if our state government also issued "pro-choice" plates, but they don't. Come on, Virginia, you're a blue state now; get with the program.

The above should not be construed as an invitation to get into an argument about abortion or politics.

But the one VA specialty plate series I have hated above all others is the one that reads, in some sort of multicolored crayon font, "Kids First."

My reasons for raging about such a thing are complex; basically, I don't agree with "kids first." We have too much emphasis on kids as it is. We're not supposed to be adults living in a kids' world; they're supposed to be kids living in an adult world, and preparing for it. And too many people use "for the children" as a shield to mask their own Puritanical dislikes.

So, when I saw this plate,

I about tore a muscle laughing

I honestly can't remember if I saw it first on the road, or on the internet. I suspect the latter; there are over 7 million registered vehicles in Virginia, and besides, if I'd seen it on the road, I would have wrecked from laughing so hard.

Like most states, we're pretty picky about questionable tags. You can't get "FUCK," for example, or racially-charged terms. There are procedures in place to stop those before they ever get stamped. Somehow, though, this one got through.

At least, it did until some Puritanical wet-nose decided that "Eat The Kids First" was a sexual reference, and got the tag retroactively canceled.

You have to have a certain sort of mind to believe that it's a sexual reference. I don't have that sort of mind. I envisioned a zombie apocalypse, not a massive orgy of statutory rape. The thought never ever crossed my mind, and I have an exceptionally dirty one. In retrospect, I'm not sure that a joke about cannibalism was any better. Still, it was, obviously, a joke.

But it crossed someone's filthy, disgusting mind, and so there came to be just a little less humor on the road. Not in the world, though; as you can see from the link above, the plate is immortalized in pictures on the internet. And from what I've seen, similar ones have slipped through the cracks in other states, too.

It might be tempting to point out that I expressed a dislike of other kinds of specialty plates, so isn't it hypocritical of me to rail against someone else's objection to one? Well... consider that I have never tried to get any kind of license plate canceled, and maybe you can see that there's a difference. We don't have the right to not be offended. I'm perfectly capable of hating something without getting all activist about it. In fact, it's a core theme of my personality.

Which is not to say that I willingly support businesses run by people with what I consider the wrong politics. I just don't expect legislation to back me up on my boycotts. But that's another topic.

And it looks like the business that provided the above prompt probably got similar backlash. I risked getting put on a List by typing "CHOP kids first" into Google, and one of the results starts out: "At the CHOP Primary Care practice (formerly Kids First) in West Chester, PA, we believe that every child should have a medical home..."

Fortunately, Kid Sex Change

is apparently still in business, for those of us who have to giggle at such things. Word spacing, people. It exists for a reason. Use it! Or don't, and risk the juvenile attention of the internet.

6 Like • Comment • View 3 comments

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