Complex Numbers (Book)

Blog Calendar

◄ September ► 2020
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!

about 3 hours 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

about 5 hours 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 23, 2020 at 12:12am

#993982

The Equation of Spontaneity

Superlatives can be difficult to remember.

PROMPT September 23rd

What is the most spontaneous thing you have ever done?

In this case, there's an added level of difficulty: to me, something is either spontaneous, or it isn't. While I dislike the idea of binary thinking, this one's pretty clear: either I plan for something, or I don't.

I suppose "least spontaneous" would make more sense, since perhaps you can think of something that you've planned longer than anything else. For me, that would probably be my professional engineering exam. Planned for it for, what, something like 15 years?

On the other end of the scale you get what I did yesterday: I was sitting there messing around on WDC when the thought came to me, "My car just passed inspection and is in working order again. I've got nothing pressing to do here. I want to take a drive." And so I selected a random destination, got dressed and took off. Planning time: oh, maybe 20 minutes to generate the coordinates and get dressed for driving. That's probably as spontaneous as I get.

If you count things that don't require any preparation at all, maybe you can count the times I've been like, "You know, I could sure use a beer right now," so I open the fridge and pop a cold one. Total time between thought and action: maybe 15 seconds, depending on where I am in the house. Less if I get the idea whilst standing in the kitchen. I guess I was assuming that the prompt is about going somewhere.

Consider, then, an equation that takes into account the amount of planning and the distance to be traveled. Less planning, higher coefficient. Further distance, also higher coefficient. Call planning time P and distance to be traveled D, then the "most spontaneous" thing would be whatever has the highest value of S (for spontaneity) = D / P (because if P is in the denominator, then a lower P means a higher value of S).

Now, in the Before Time, I have considered upping and taking off to Paris or something on no notice, because I could. I mean, I have an up to date passport, and they were still letting Americans in. But since I've never actually done that, we'll reserve that particular value of S for sometime in the future. I hope.

I don't know, maybe D should be T, for time. After all, if I decide to drive to Los Angeles, it's about 36 hours of driving, or call it four days of perfectly reasonable 8-hour drive times. Paris is almost twice as far away from me as L.A., as the plane flies, but it's about, oh, call it 12 hours from my house, to airport, to the inevitable connecting airport, to de Gaulle, to, I dunno, say the Eiffel Tower because everyone knows it's in Paris. (I've always despised when movies have to show both an establishing shot and the full name of the city. It's like *pic of Eiffel Tower* "Paris, France" "REALLY? I HAD NO IDEA!!!" *pic of Sydney Opera House* "Sydney, Australia." "Fuck me, I thought that thing was in Toronto.")

But I digress. The point is whether you consider distance or time, it's still in the numerator of the equation: more time or longer distance, divided by the planning time.

Now that I think of it, sure, it should be time. That would put S in units of time / time, making S (Spontaneity) dimensionless. That makes sense from an engineering perspective, since there are no actual units of spontaneity. Otherwise it's distance / time, which could be confused for speed.

So I'll go with the time a friend of mine called me (we did that sort of thing back then) and said, "Hey, we've got tickets to Dar

Williams in New Jersey, wanna go?" So I threw my shit together, took off, met my friend and her friend, and we all drove up to northern Jersey together. Total travel time, maybe 9 hours. Prep time, 30 minutes. S=9/0.5=18. There, that's my record so far (at least that I can remember). That's just getting there, though. I'm not counting being at the concert, meeting Dar, or the drive back (which I was asleep for most of anyway).

It's unlikely I'd ever beat it myself, because I have cats and at a minimum I'd have to arrange for someone to care for them when I'm away for more than half a day or so.

Anyone who can beat S=18, let me know. That is, if you're still here after all the math.

9 Like • Comment • View 9 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.