Complex Numbers (Book)

Blog Calendar

◄ October ► 2019
S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

a day 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

a day 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.

October 16, 2019 at 12:25am

#967929

Tower

https://www.cracked.com/article_26631_the-coolest-scientist-in-history-youve-nev...

The Coolest Scientist In History (You've Never Heard Of)

Okay, I'll grant "cool," but I wasn't ignorant of this guy's existence. Still, there's no harm in learning more, right?

Imagine that it's the late 1800s, you're living in some godforsaken Russian backwater, and as far as your barely educated ass knows, the greatest technology in human history is vodka.

To be fair, at that point, the greatest technology in human history was vodka.

Meanwhile, the teacher down the road is mumbling to himself about elevators to space, flights to the moon, and mankind achieving blissful immortality among the stars. And here's the kicker: He's not even drunk yet! Who the hell is this guy? He is Konstantin Tsiolkovsky.

There you go, the name. Now you don't have to visit the article, but you still should; I'm not going to quote the whole thing because copyright and such, and Cracked is funny.

After three years of study, Tsiolkovsky passed a teacher's exam and, assigned to a village that made the middle of nowhere look luxurious, began the profession that would sustain him for the rest of his life. When not teaching, he tried writing his own science fiction, but he kept getting distracted by the accuracy of the "science" half.

I feel yah, Konstantin. Every time I write science fiction, it goes something like this: *science thing as a plot device* "Wait, that can't work." "But can it?" *hours of wikiderp* "Just write it, Waltz." "But it's implausible!" "Just. Write. It. Waltz." And Tsiolkovsky didn't have Wikipedia.

Never forget that the future will always be a bizarre mix of the predictable and the baffling.

Truth.

But good ideas can come from anywhere at any time. And that's how someone born 162 years ago played a big part in developing both real-life technology and many of the sci-fi tropes you enjoy today.

One thing the article doesn't mention: Arthur C. Clarke, whom I'm certain you have heard of, stole from Tsiolkovsky for one of his early novels, detailing the construction of a space elevator, or, as those of us who did know about dead Russian scientists call it, the Tsiolkovsky tower. You might recall that Clarke, too, was a visionary, probably most famously for either proposing the idea of geosynchronous communications satellites, or saying "any sufficiently advanced technology is indistinguishable from magic."

There are technical issues about space elevators that continue to make them impractical, but I have no doubt that if we don't nuke ourselves back into the stone age, one day we'll have the technology to build a tower into orbit.

Like • Comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.