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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

September 22, 2022 at 12:01am

#1037978

Survival

Again with the (shudder) outdoors.

Timeless Survival Skills
These classic tips will help you survive and thrive in the wild

1. Don't go in the wild.
2. See #1

But I suppose people don't heed this advice (or any other), and they find themselves over a mile from the nearest 7-11 from time to time, so it's important to know how to survive in such a situation.

As far as I can tell, the article actually provides helpful how-to instructions. I wouldn't know, because I don't intend to ever be in the kind of situation that requires them ever again, so I'm not double-checking.

1. Navigate with a Map and Compass

Triangulation has kept outdoorsfolks found and alive as long as magnetized needles have been pointing north, and it’s still the most effective method of getting unlost that doesn’t involve an orbiting satellite.

I love GPS. I think it's the greatest invention since beer (sliced bread doesn't even come close). But one cannot rely solely on it; batteries die, and satellites get shot out of the sky. I know how to read a map. Hell, I even know how to fold one.

2. Call for Help with a Signal Mirror

Long before the era of SIM-card GPS messengers, calling in the cavalry required little more than a shaving mirror and a rudimentary grasp of Morse code.

Difficulty: receiver needs a rudimentary grasp of Morse code. I mean, all I know is S, O, and S, but hopefully that would be enough.

3. Live to Tell the Tale

My closest call in 40 years of wilderness travel came about—not surprisingly—on a Field & Stream assignment in Alaska.

Reading this author's harrowing story would be enough, by itself, for me to limit my exploration to areas with breweries nearby.

4. Learn How to Snare a Rabbit

Or—and bear with me here; this is complicated—always know where the nearest grocery store is, making sure it's not more than a couple of miles.

5. Make a Tinder Bundle

Sadly, this has nothing to do with a popular hookup app.

Timeless Gear: The Old Flame

The Doan Magnesium Fire Starter was invented in 1973 by an outdoorsman named Sol Levenson, who came up with the idea while on a trip to South America...

I went through that entirely irrelevant-to-me article only to find it was a crummy commercial!? Son of a bitch!

3 Like • Comment • View 2 comments

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