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Wednesday, Jul. 31, 2024

3:59pm EDT

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

Averren

about 2 hours ago
In response to "Forgotten Food"

Cultural appropriation? Of foods? Hogwash.

Elisa: Middle Aged Stik

about 3 hours ago
In response to "Forgotten Food"

The issue of people appropriating Black and Indigenous foodways is one of the few areas where I tend to have the most conflicts with the pro-GMO crowd. Some members of that cohort feel that there is plenty of experimentation/crop development to be gleaned from Indigenous heirloom crops. While I think there's likely truth to that, I worry that they are not considering the agency of Indigenous peoples and perhaps working with them to work out an agreement of some sorts. There are fewer crop-related issues when it comes to Black foodways (for now), but the pro-GMO crowd sometimes comes across as perpetuating racist stereotypes about scientific knowledge in the Black community, which in turn has created an opening for the pro-organic crowd (something I'm very unhappy about since it's setting unrealistic expectations from a personal finance point of view).

1 Like

Aiva Raine

a day ago
In response to "The Habits of Nones"

I'm not sure their consensus that higher income equates to a greater disbelief in a higher power is correct. I suspect that having a greater income insulates you from many things- not just the need to believe in a god or gods. You are probably correct in that money does allow more freedom from things people fear- and religion is all about fear.

But I know plenty of people from all income brackets and it seems more and more are slowly trending towards an REM song.

Regardless of the breakdown/income levels- whether the 30% mentioned in the article is atheist, agnostic, couldn't be arsed to care, or used to go to church, but now don't- I'm glad it's that high now. It means things will start to change soon since we have a large enough group of people to effect social change and said group doesn't make decisions based out of fear of imaginary beings torturing them for infinity.

2 Like

Elisa: Middle Aged Stik

a day ago
In response to "The Habits of Nones"

"Unfortunately, by strict application of that definition, monotheists would also be covered, as they do not believe in "gods" but in one "God."

So you see where some of this confusion might be coming from?"

I think that's not much strict as pedantic, myself, partly because at least in writing the lowercase "gods" is clearly being used as an all encompassing term for higher power figures across all belief systems. Would deities have been clearer? Maybe, but it's a word that not everyone involved in such a discussion might recognize. Sometimes the tradeoff in diction creates loopholes like this, but those loopholes may end up being a nonfiction in the long run.

1 Like

🌕 HuntersMoon

a day ago
In response to "The Habits of Nones"

I'm a dyslexic believer... I believe in DOG!

2 Like

Brandiwyn🎶

a day ago
In response to "Unbelievable?"

Re #3 - As a PWP ("Person With Parkinson's"), I can say that no amount of thinking hard about a muscle will help you control that muscle if you don't have adequate dopamine to send that message through your nervous system.

1 Like

Brandiwyn🎶

a day ago
In response to "Unpredictable"

"But I do wonder how one would design a random point generator where every point on the surface of a sphere is equally likely." This sounds like a differential equations problem, but hell if I remember anything from that class.

1 Like

Elisa: Middle Aged Stik

Jul 28, 2024 at 11:18am
In response to "Revisited: "The Truth is Out There""

Sometimes, I make an effort to avoid reusing a title, but much of the time, I can't be arsed.

I may "repeat" titles for multiparters, but somehow I've been able to avoid reusing titles over, um, over 3400 entries.

I still have mixed feelings about PZ Myers. He still bothers me less than the turd nugget who spawned my whole Atheist vs. Atheist series, though.

1 Like

tj ~ HiLo Silver - Away!

Jul 27, 2024 at 3:44pm
In response to "Unbelievable?"

Muscles Grow More When You Concentrate on the Mind-Muscle Connection, I wonder if this also applies to balls?

2 Like

Adherennium Dr of Phoolishness

Jul 27, 2024 at 2:21pm
In response to "Still Planning"

Much underrated in searches is the useful - sign. 'Paris -Olympics' might help.

3 Like

July 10, 2024 at 10:03am

#1073780

Phrase Turner

It's only been about a month, and I've already forgotten why I saved this articlebook ad from CNBC. But I'm sure I'll have some things to say, anyway.

Former CIA agent: 4 powerful, underutilized phrases can help you establish credibility and earn anyone's trust

In my career as a CIA analyst turned CEO and business advisor, understanding how to communicate effectively in complex and stressful environments has been at the core of everything I do.

That, and knowing how to spy on the competition without getting caught.

Ultimately, I've found that by leading with honesty and authenticity — and with some practice — anyone can learn how to meaningfully earn the trust of powerful stakeholders, and get them on your side.

Yep. People respond positively to honesty and authenticity. So once you've learned how to fake those things, you're golden.

Using these four key phrases have helped me become a better speaker and problem solver...

Oh, that's right. I thought this might be of interest to writers, as phrases are our stock-in-trade.

1. 'What information do you need?'

This has the added benefit of preventing you from giving away too much information, yourself.

I remember asking Senator John McCain this question during a foreign policy briefing once.

Nothing like name-dropping to show your street cred. "Yeah, I once had a casual conversation with a guy who at one point was just a few electoral votes away from becoming President."

2. 'Is there anyone else who needs to be part of this discussion?'

"Do you need to bring your mother here?"

3. 'Who disagrees?'

"And what dirt can we find on them to make them change their minds?"

4. 'I don't know, but I will find out and come back to you'

Okay, I can't really snark on this one. That's engineer-level thought right there. No one knows everything, and it's better to admit that you don't know than to make something up that might come back to bite you.

Just be sure to actually follow through.

Seriously, though, I don't think it's a bad articlead. And even I was impressed at the author's credentials at the bottom of the page. I just couldn't let certain jokes sit there, bored, with nothing to do.

6 Like • Comment • View 3 comments

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