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 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 10 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 22, 2021 at 12:02am

#1012324

Imperial Decree

I don't really have a whole lot to say about this link, but I'm putting it here for those benighted souls who have never heard of Emperor Norton. Behold:

6 Details About America's First, Only, And Greatest Emperor

Although I had heard of Norton I, there were still details in this article that were new to me. Of course, it's still Cracked, so I wouldn't take anything here as absolute fact without verifying it, but I know that he indeed existed, and in general, the biography checks out.

The year is 1859. The United States is on the verge of a massive split that will eventually lead to the Civil War. As lines are drawn and tensions are running high, a man in San Francisco writes to the local newspaper. His name is Joshua Abraham Norton, and his plan is nothing short of grand. He declares himself Norton I, Emperor of the United States. Many have never even heard about the reign of the United States' first and only monarch ...

Like I said, not a lot to paste here, so I'm not even going to go over the Cracked-standard numbered list highlighting.

Several times over his 21-year reign, he called for bridges to be built and streets to be repaired, as The Emperor knew that his empire needed strong infrastructure.

Many recent government administrations should have learned that lesson, but didn't.

Also, it should be noted that Norton was actually quite progressive for the time, and honestly, he deserves praise for that in a way that most people from that era don't deserve. He advocated for the rights of Black Americans in his proclamations, and he fought back against the violence that Chinese immigrants faced in San Francisco.

Ditto for this.

This story had the potential to get kind of ugly. A delusional guy parading around the city as a monarch who was also frequently publicized in papers for laughs? This sounds like it's just going to be a story about how much people made fun of him. Here's the thing, though: they really didn't. Yeah, people found it funny that he was acting out some royal fantasy, but honestly, they loved him. He became a sort of symbol for the city, and residents were excited when they saw him walking around, almost as though they had a brush with a real monarch.

Pretty sure that's a San Francisco tradition that continues to this day. Though they don't do much for the homeless now. Maybe if said homeless dressed up as Emperors... nah.

The Emperor Norton Trust is a nonprofit dedicated to preserving his memory, and there have been campaigns in recent years to rename the Bay Bridge that connects San Francisco to Oakland in his honor.

I'd get behind that.

Anyway, like I said, good read, and a quick one. Perhaps tomorrow I'll end up posting something I could make more in-depth comments on, but for now, just bask in the glory.

3 Like • Comment • View 2 comments

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