Complex Numbers (Book)

Blog Calendar

◄ February ► 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
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:

Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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

February 3, 2019 at 1:35am

#951042

Georgia Not On My Mind

Talk about your plans for the superb owl or if you're not a fan talk about something you are a fan of like maybe Adam Levine or Gladys Knight she's doing the national anthem.

You know what I'm not a fan of?

Atlanta.

Oh, the city's nice enough - if you can move around in it. Which, if you're driving, you can't. You think NoVA is bad? You think Boston is bad? You think Orlando is bad? Phoenix? L.A.? Well, you're right, but for unadulterated frustration, try driving in Atlanta. You know how Yoda was all like, "Do or do not. There is no try?" Well, Atlanta is firmly in the "do not" camp when it comes to driving anywhere.

I can only imagine a sportsball game would make things worse, even if it does take place on a Sunday.

And yeah, I'm not a fan of football. Oh, don't get me wrong; I understand that many people are, and I'm not trying to dis your hobbies. You like to make fun of me playing D&D and reading comic books, so I'm taking the moral high road here, because I'm the better person.

I can even understand why people who aren't normally fanatics about football get together on a certain Sunday early in the year to watch the game whose name we can't speak without incurring the wrath of the NFL's lawyers. I even attended such a party once in this millennium, because Springsteen was doing the halftime show, and there was no way I was going to miss that. Also, there is traditionally drinking involved, and I encourage such behavior whatever the excuse (or lack thereof). So yeah, party on, Garth.

I get that people are into the spectacle and get emotionally invested in the whole thing. I feel that way about some rock concerts.

But what I can't grok, not even a little, is why people watch the game for the fucking commercials. I hate ads with an all-consuming, fiery passion, to the point where I didn't even watch TV at all for many years so as not to encounter a commercial. I only started up again when streaming became a thing, because there are no gods-be-damned ads. I freaking pay for TV shows that I like on Amazon because I don't have to put up with commercials. While I do understand that there are a lot of innovative ads in that spot, they are still ads and thus need to be incinerated in the burning pits of Mordor. And then I hear things like "Oh, I don't care about the game; I just want to see the commercials." WHAT EVEN GAAH I LITERALLY CANNOT.

As an aside, if any other activity - chess or math, e.g. - caused the kind of injuries to grade school students that football does, it would be banned. I'm just saying. That's not my issue with football, though. It has more to do with it being a four-hour delivery system for commercials with about 11 minutes of actual sports action.

But you know the absolute worst thing about the big game? I'll tell you what the worst thing is, and it's a very personal one. You see, the very first one was held the same year I turned 1 year old. If you count that as number 1 (or "I"), then you can quickly see that whatever the game number is in any given year, I will be turning that old a few short days later.

That is a reminder that I simply do not need.

Also, who in the ad-saturated hell is Adam Levine? I can't be arsed to look him up.

5 Like • Comment • View 5 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.