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 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 5, 2022 at 12:03am

#1036122

Logos

I have only a passing interest in marketing, and suck at graphic design, but I find logos interesting. So, apparently, does Cracked.

The Bizarre Origins of 15 Famous Logos

"Bizarre" is too strong a word here, but such are clickbait headlines. You won't believe what happens next!!!

In the quest for that perfect logo that will stand out but not in a bad way, companies have reached back into the scary, briny depths of human creativity, taking inspiration from everything from strip clubs to Greek gods.

So there you have it: the answer to the question (which nobody ever asked), "What do strip clubs and Greek gods have in common?" (Other than "Both will smite you if you put your hands somewhere you shouldn't.")

I'm not quoting all fifteen here. Just the ones I have something to say about.

14. Chupa Chups

You’d never know it from the lack of ants or anything decaying, but the Chupa Chups lollipop logo was designed by Salvador Dali during his “anything for money” phase in 1969.

This one, I knew. (Actually, I think I knew most of them, but there's always something else to learn.)

12. Starbucks

Hopefully everyone knows by now that the original "mermaid" was bowdlerized to appeal to prudes. What might be news is where the big-titted mermaid originally came from.

It probably actually came from the artwork in a 15th-century German book.

"Probably?" Okay.

Speaking of titties...

11. McDonald’s

The golden arches were adopted as an ode to the ones that framed the original restaurant, but they were kept because they were Freudian. During a branding overhaul in the ‘60s, one psychologist advised them to keep the logo because it “symbolized a mother’s nourishing breasts.”

We're talking about two of the biggest franchise chains in the US, and thus the world. The moral of this story is: boobies work.

9. Michelin

This mind-blowing about the Michelin Man comes in four parts: 1) He has a name. 2) That name is “Bibendum.” 3) He’s made of tires. 4) He partied like a rock star. Early advertisements featuring the Michelin Man from the late 19th century often depicted him smoking a cigar and drinking champagne...

I think they accidentally a word there. Also, the Michelin Man is apparently a badass. Or was, until they turned him into a marshmallow.

8. MGM

The first MGM lion was apparently such a beast that he was buried under a marble slab to “hold down the lion’s spirit,” as if it might leap out and turn someone awesome via possession, but that’s nothing compared to the next one, who was the first to actually roar.

As far as corporate logos go, it's hard to beat an actual lion. (Food Lion, aka Shitty Kitty, doesn't count.)

Why hasn’t Marvel given this guy a movie?

For the same reason Cracked doesn't do an exposé on Alfred E. Neuman: competition. Marvel is owned by Disney, and the Mouse has more lawyers than a lion can eat.

3. Facebook

“Blue is the richest color for me -- I can see all of blue,” he later explained, because that’s Mark Zuckerberg’s top business concern: Mark Zuckerberg.

Colors aside, I always hated the facebook logo's font.

1. Gucci

Those two interlocking G’s don’t just stand for the brand name -- they’re actually the initials of the founder. Yes. The poor man’s name was Guccio Gucci.

And based on the movie House of Gucci (an MGM film, incidentally), you could probably power all of Florence if you attached a dynamo to his spinning corpse. To be fair, insiders have said the movie's not accurate, but at least you got to see Lady Gaga's boobies.

3 Like • Comment

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