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!

4 minutes 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.

Adherennium Plotting something

about 2 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.

May 6, 2024 at 9:44am

#1070601

Brain Farts

I think my random number generator is determined to clear out all the Cracked links from my queue.

5 Deaths That Make You Say, ‘Well, He Was Asking For It’

That's a comedy site, and death is very much not funny... except when it is, like when someone falls off a cliff trying to take the perfect selfie.

When someone brings about their own downfall, people sometimes say they were hoisted by their own petard. We avoid using that expression ourselves because what exactly is a “petard” anyway?

Now, that's French I knew before I started learning French. The first translation I heard was "little fart." The linked article goes into more detail. Not about farts, but the word "petard."

5. The YouTube Demonstration of How Bullets Can’t Go Through Books

We like to make fun of those damn kids and their tikkytokky, but people posted Stupid Human Tricks on YouTube since approximately the day it was released.

This particular one, though, is from 2017, well over 10 years after the site launched.

As for Ruiz, he will sadly never get to fulfill the promise he made with some of his last words: “Every week, I’m gonna be bringing you guys new videos!”

This is why I never make promises. As soon as I start to do so, my mind goes to all the dumb ways I could die and thus break the promise. I'd rather die than break a promise, so I avoid having to make that choice.

4. The Thieves Who Stole Cobalt-60

You know, this wouldn't be the karmic justice that it obviously is if it had happened back when Marie Curie was doing her Nobel Prize-winning shit. But this was in 1999, long after Chernobyl, and in another part of the former USSR.

One of the thieves dropped dead within 30 minutes. This was the member of the gang who actually held the material. Sources differ on exactly what happened to the rest, with some saying that two others died next. At least one thief did survive, which meant he went to the hospital and then got arrested.

And sadly, not sentenced to help clean up Chernobyl.

3. Ripping Down a Crash Mat, and Crashing

In case it wasn’t obvious, all the men had been drinking.

Don't freakin' blame booze for this. Booze enhances what's already there, be it stupidity, like these guys, or, in my case, genius.

2. The Trophy Hunter, Crushed by His Trophy

Every so often, you’ll hear about some rich American going to Africa to kill a big-game animal and pose with the kill. Theunis Botha was not one of these casual trophy hunters. Botha was an expert trophy hunter, who led hunts in Zimbabwe and South Africa for decades.

This one is satisfying on at least two levels. Not only do we get treated to jungle justice, but also we can make "Many Bothans died" Star Wars reference jokes.

1. Joseph Stalin, for Being Stalin

One of the few good things you can say about Adolf Hitler is that at least he killed Hitler.

Apparently, one can say something similar about Stalin, only his victim was Stalin. It was just a little more indirect, in his case. Kind of a Rube Goldberg self-destruction machine.

His staff did not summon his personal physician. They couldn’t, as the man was currently being tortured in the basement of border security headquarters.

There's a lot more fatal idiocy you can read about at the link that contributed to his death, but ultimately... he was hoist by his own petard.

3 Like • Comment

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