Complex Numbers (Book)

Blog Calendar

◄ June ► 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.

June 7, 2019 at 12:44am

#960316

Moving Right Along

Sorry I’m late.... was busy with other stuffs and driving around tonight.

With that said... what is your favorite method of traveling, and why?

I quoted the entire prompt above, not to call out the prompt-giver (Dragon is hiding is cool, and so is every other judge over at "Invalid Item"

) but because it's relevant: My favorite method of traveling is... wait for it... driving around.

Of course, there are some exceptions here. I still can't drive to Hawai'i. Or, well, most islands. Hell, entire continents. They keep talking about building a bridge across the Bering Strait, which would in theory link the bulk of the world by road, but, well... Russia and the US aren't exactly on "drive-across-the-border" terms right now.

Another exception is that I won't drive if I've been drinking, not only because it's illegal, but because I'm not a fucking asshole. Well, not when it comes to endangering others, anyway. But even then, I'm happy to let someone else drive.

When I'm in a city like New York, I'm fine with using public transportation. Driving in NYC isn't as bad as you probably think it is; the problem is finding a goddamn parking spot. So, sometimes, when I go to NYC, I take the train. That's a pretty relaxing mode, usually.

As for flying, well, I love the "flying" part, and despise the "everything else about it" part. Leave it to humans to figure out how to use SCIENCE to freaking FLY and then turn the experience into a bloody nightmare.

I think I'd like traveling by ship, but see previous entry on cruises to contrast the ideal of the cruise with the reality. But I love being on the water, provided of course I'm protected from the accursed daystar.

There are, of course, other modes of transportation: bike, horse, rocket, elephant, rickshaw, camel, lysergic acid diethylamide... all of them have their place. I rode an elephant once, by the way. It's... an interesting experience, being that high up. Not scary at all, but I'm not afraid of heights. I do have some concern about being trampled, but that's kind of hard to accomplish when you're on the other side of the elephant from the tramply bits. I rode a camel once, too, but that was a very long time ago; I think we were being chased by a saber-toothed tiger.

But driving... well, I do like the feeling of being in control of my route and destination, however illusory that might be sometimes. I should emphasize here that this is not about safety - I'm aware that driving has its hazards, and is far more likely to kill or injure than some of these other transportation options. Life is inherently risky; you also have a good chance of dying if you stay home and go nowhere. Well, technically, you have a 100% chance of dying, regardless, but hopefully you know what I mean.

More than that, though, is the scenery. From an airplane, you see airports, the sky, clouds, and this big round thing below you. On a boat, you're surrounded by ocean. A train provides some scenery, depending of course on the route (I highly recommend NOT looking out the window whilst riding on a train along the Northeast Corridor), but even there you're usually limited to a narrow field of view.

And, of course, with driving you're not limited. I know a lot of people like to leave point A and take the most direct, most efficient, fastest route to Point B, and they're done. That's fine, but that's not me. I purposely go off on side trips, and sometimes I avoid interstates (usually the fastest way) entirely.

Because, to me, there is no such thing as a "destination." There is only the journey.

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.