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

October 19, 2020 at 12:01am

#996208

Juxtaposition

Entry #8 of 8 in

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

hairtherapy@gilbertneurolgy.com

There exists an animal called the Japanese Dwarf Flying Squirrel.

Each word in its English name has a specific meaning:

Japanese: from Japan
Dwarf: smaller than usual
Flying: able to soar
Squirrel: Cute rodent with bushy-ass tail

Nothing really special about any of these individual words. Quite common, actually. We see examples of most of them every day, either in our backyards or on the internet. Well, maybe I see more Japanese than others because... well, just you never mind.

The point is, put those words together and you get Epic Awesomeness. A Japanese Dwarf Flying Squirrel. Seriously, go to that link above and look at it. LOOK AT IT. And look at this picture,

too.

If that is not one of the cutest, if not THE cutest, thing you have ever seen, there is something seriously wrong with you. Possibly even a neurological disorder.

Perhaps, then, you need hair therapy.

See, unlike four words forming a unique synergy, as with the squirrel, sometimes you get four words that make you go... "Huh?"

Hair - humans' answer to fur; some have more than others
Therapy - a process to help restore a person's mind or body
Gilbert - somebody's name, presumably
Neurology - the study of the brain and nervous system

Each one of those words, taken individually, is rather innocuous -- though my personal connotation of neurology stems from when they took out part of my ex-wife's brain.

Taken together, though, they make no sense, not even a little.

I am, however, reminded of the hairshirt that penitents supposedly wore, and perhaps still do. Something deliberately uncomfortable that focuses the mind, hopefully forcing one to contemplate the numinous and esoteric rather than the pleasures of the flesh.

As a dedicated hedonist, though, I prefer cotton or silk. Just not squirrel fur. That would be cruel.

Mini-Contest Results!

I appreciate all the comments, but only one seemed to address the question in my last entry. So today's Merit Badge will go to WakeUpAndLive~doingNaNo'24

for:

Scientists discovered how to control a biomechanical hand, just by thoughts- 2009

Amputee Pierpaolo Petruzziello learned to control a biomechanical hand connected to his arm nerves with just wires and electrodes and became the first person to make movements like finger wiggling, making a fist, and grabbing objects using just his thoughts.

Which is truly cool (and, serendipitiously, ties in to the "neurology" thing in this entry, which was chosen at random). However, can you imagine what would happen if someone figured out a way to hack it?

"Why are you punching yourself?"

5 Like • Comment • View 5 comments

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