Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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.

September 10, 2019 at 12:04am

#965912

Facts

PROMPT September 10th

Today’s prompt was submitted by LdyPhoenix

!

What are some of the weirdest facts you've ever learned? Wow us with your bizarre knowledge!

Today's vocabulary word, boys and girls, is epistemology.

Essentially, that's the study of how we know what we know.

I bring this up because possibly the weirdest fact I ever learned is that we don't know how we know what we know. If that makes any sense. If it does, then congratulations; you're eligible to become a philosopher.

"Fact" is a slippery concept, and I don't just mean for politicians. Most concepts are slippery, I think, if you examine them too closely. It's like... you can see a cat and identify it as a cat, but when you zoom in really close, all you see is the fur. And fur could belong to any number of animals. And what's an animal, anyway? At the smallest scales, the lines get blurred.

This is especially true if you keep zooming in. Eventually, you get to molecules and atoms, and then protons, neutrons, electrons - what we commonly call the building blocks of matter. Zoom in further on a proton or a neutron, and you get to quarks, which are more like electrons. What I mean by that is, not only do we not know where a particular electron or quark is at a given moment, we can't know where it is at that moment. It's all smeared out in a probability distribution.

At that scale, even the distinction between matter and energy is fuzzy. And also the distinction between "is" and "isn't."

How, then, can we know anything?

As I've mentioned before, I only claim to know anything to some degree of probability. I live in Virginia, so I'm close to 100% certain that Virginia exists. But then, what is this concept of "Virginia?" An area enclosed by a surveyed boundary, probably, or perhaps the political system, or its checkered history.

I've been to New York City, so I'm pretty sure it exists, too, though less certain than I am of Virginia. And I've never been to Afghanistan, so I have to take other peoples' word that it exists. I don't have a problem doing this. But if you came up to me and told me you've been to the lost continent of Atlantis, I'm going to need more in the way of confirmation.

So it is with anything we take as "fact."

At some point, to avoid falling down the rabbit-hole, you have to put things in different boxes: "reality," "not-reality," "save for further investigation." But we all tend to put different things into those boxes. Flat-earthers come to mind; the idea of a somewhat spherical Earth goes into the "not-reality" box for them (unless they're just fucking with us, which is a possibility we have to consider). Meanwhile, sane people put the round Earth into the "reality" box. Other people might accept as absolute truth the literal existence (as opposed to the literary existence, which is largely undisputed) of fairies.

Science helps with that sort of thing, but one has to be open to its findings, as well - though science, and science reporting, are not without their problems.

So I don't know if that qualifies as "bizarre." I think it does, if you give it real thought - the idea that there might always be limits to our knowledge, and that facts are actually probabilities.

2 Like • Comment • View 2 comments

© 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.