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 8 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.

March 24, 2024 at 8:15am

#1066834

Revisited: "Took the train down to Athens"

Today is the day when I dig into the archives for a past post and talk about what's changed—in me or in the world.

Unfortunately, what's changed in this case is that both of the links I shared are now broken: "Took the train down to Athens"

, from 14 years ago.

On one talon, it should be no surprise that 14-year-old links are broken. On the other talon, they were from The Daily Mash (kind of the British version of The Onion, still in existence) and Cracked (which, though it's gone through its own changes, I continue to read and, on occasion, share).

Everyone knows that Greece's economy has taken a turn for the worse, right?

I reiterate: this was 2010. Lots of economies had already tanked. Some had even begun to recover.

(There followed a movie reference that was probably a lame attempt at a joke even way back then.)

But it's the next-to-last paragraph that had me rolling on the floor laughing my acronyms off.

And sadly, whatever that funny bit was is probably lost in the mists of time. Someone might be able to find it by searching the internet archives. But that someone will not be me. The world has moved on since then, and there are more relevant jokes around. Besides, I just can't be arsed.

Bonus link is from Cracked:

Back then, that site ran Photoshop contests that schlubs like us (not me, though, because I suck at photo editing). This was apparently one of them.

Incidentally, The Daily Mash was paywalled last time I tried to look at it (it's been a while). They're funny, but not funny enough for me to subscribe.

The title of the post was, as with some of my other entry titles, a reference to a song. If you feel cheated by all the broken links, at least I can post the relevant music video, Euro-Trash Girl from Cracker, who I once had the pleasure of seeing in concert:

Took the train down to Athens
And I slept in a fountain
Some Swiss junkie in Turin
Ripped me off for my cash
Yeah, I'll search the world over
For my angel in black
Yeah, I'll search the world over
For a Euro-trash girl

2 Like • Comment • View 1 comment

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