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Thursday, Nov. 21, 2024

2:46pm EST

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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:

Robert Waltz

about 24 hours ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

a day ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

October 23, 2024 at 8:02am

#1078781

Known Unknowns

Comedy meets science in another Cracked article.

Questions It Looks Like Science Is Never Gonna Be Able to Answer
Those eggheads aren’t so smart after all, are they?

Right, because not knowing everything is the same as knowing nothing.

Science isn’t a discipline known for moving fast, breaking things or shooting first and asking questions later.

Well... kind of. For various definitions of "fast."

4. The Riemann Hypothesis

It’s ridiculously complicated, but let’s just say that according to the hypothesis, proposed by Bernard Riemann, there’s a pattern to the distribution of prime numbers along the number line.

Oh, come on, that's not science; that's math, a separate discipline that will never know everything.

3. Goldbach’s Conjecture

If 160 years seems like a long time, try 282. That’s how long ago Russian mathematician Christian Goldbach theorized that “every even positive integer greater than 3 is the sum of two (not necessarily distinct) primes.”

I invented the principle "never let facts get in the way of a joke," but again... math, not science.

2. The Clarendon Dry Piles

It sounds like a sex act that only exists on Urban Dictionary, but it may be even weirder. It’s two brass bells connected by a pair of batteries called dry piles powered by electrostatic forces. The amount of charge carried between the bells is so small that it appears to be a perpetual motion machine, but the truth is, the batteries are just draining extremely slowly.

So science has, in fact, answered a question: extremely slow drain. At least this one is actually science, not math.

It’s anyone’s guess when the batteries might die, but we’ll probably never know because the hardware will probably break first.

Seems to me that question will eventually be answered, so this section still doesn't meet the promise of the headline.

1. The 500-Year Microbiology Experiment

Also science.

It’s a stunning act of futility and optimism to bet on society surviving another 500 years, but that’s what scientists at the University of Edinburgh did in 2014 when they endeavored to find out if certain strains of dried bacteria can survive five centuries.

This headline sucked. That's another question that will eventually be answered.

That is, if, as the article notes, science is still around in 490 years.

7 Like • Comment • View 2 comments

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