Complex Numbers (Book)

Blog Calendar

◄ January ► 2021
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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

January 16, 2021 at 12:01am

#1002194

Dropped

PROMPT January 16th

In your entry today, write about something you overheard while eavesdropping on a conversation you were not a part of. As part of “Creation Saturday,” you choose whether the conversation you write about is real or fake! Encourage discussion in your comments section - do your readers think your story is real or not?

Truth? I hate eavesdropping. If it looks like I might be in a situation where I might overhear something not meant for me, I nope on out of there. None of my business, even if they're talking about me. Especially if they're talking about me. I don't consider it a guilty pleasure; I consider it highly unethical, because in general, my ethical compass points to "if I don't like it when someone does it to me, I reject doing it to them." And I hate being eavesdropped upon.

That said, you don't live very long before you find yourself in such situations, beyond your control. Since I find it unethical, though, my mind revises such conversations so I can pretend they never happened. Consequently, though I know I've accidentally eavesdropped before, I can only remember one specific instance of it, and even there, I can't remember the exact words spoken.

It was late, and I don't think the boss knew I was still at the office, because I stayed in the back and mostly just concentrated on my work. I went to get a drink or use the restroom or something, and I overheard the boss and the senior engineer, in the boss's office, discussing my performance and whether to give me a raise or not. I immediately noped away, quietly, even though admittedly there was a part of me that wanted to hear what they really thought about me.

That part got quashed.

Look, I'm no saint and you know it. But mostly the things that I do that are un-saint-like affect only me. When other people are involved, my internal rules change. Like... I have no moral constraints against getting drunk, but I won't drive under the influence because someone else might get hurt. That sort of thing. And in this case, the bigger part of me would rather have remained in ignorance that the conversation ever happened (though they certainly had every right to discuss my work performance in private). It's not so much because I didn't want to know what they thought about my work; like I said, I really did. It's more because knowing would have forever changed my relationship to both of them. Hell, if I didn't like what I heard, I might have had to go looking for another job.

As it turned out, that probably would have been for the best in the long run, but that's another story unrelated to the eavesdropping. As it was, I stuck around at that company for ten more years... and yes, a couple months after the conversation I had a performance review and ended up with a raise. That boss had his issues, but as far as I know he was always honest with me -- except for one big thing that, ten years later, caused me to jump ship and go work for the same former senior engineer who was in the conversation. But that's also another story for another time, nothing to do with the topic at hand.

That said, eavesdropping and the fallout thereof makes for interesting drama in fiction, much as murder makes a good mystery even though it's wrong. And yet, whenever I see it happening, either reading about it or on a screen, it still makes me cringe.

Now, I'm supposed to encourage discussion in the comments. Sure, you can decide for yourself whether that situation was real or fake, but let's make it more interesting with a

Merit Badge Mini-Contest!

Since a lot of you reading this have already done, or are preparing to do, your own entry on this topic as part of the 30DBC, I'm going to turn things around for the contest. In the comments, tell me, not about a conversation that you overheard... but about a conversation that you participated in that was eavesdropped upon, that you wish hadn't been.

As with the prompt, I don't care if it's truth or fiction, as long as it's interesting, and the one I find most interesting and/or amusing will earn the commenter a Merit Badge.

Per usual, you have until midnight tonight, the end of Saturday, WDC time... though I can't guarantee I'll do my usual post just after midnight as I plan to drink tomorrow evening. But at some point tomorrow, someone will get a Merit Badge (assuming, of course, that there's at least one relevant comment below).

3 Like • Comment • View 3 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.