Complex Numbers (Book)

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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/

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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 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 4 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.

January 18, 2023 at 10:19am

#1043310

Survivalism

For some reason, I was simply exhausted last night and went to bed early. I suppose it's possible that it's a portent of my inevitable demise, but it was probably just the weather.

Speaking of demise, today's article, another one from Field & Stream, is about survival.

Four Survival Myths That Could Get You Killed
Our expert weighs in on some misconceptions about how to live through real-life survival scenarios

Oddly, for me at least, one of these myths isn't "It's okay to go into the wilderness."

Spend enough time in the outdoors, and you’re bound to wonder how you would handle a true survival scenario.

For me, "enough time" is about five seconds.

Could you gather and forage enough food? Could you build a strong survival shelter to keep you warm and dry? Could you start a fire…in the pouring rain?

No, no, and no.

Myth No. 1: You Can Live Solely off Natural Survival Foods

I discovered the truth of this back in college. Turns out you can't actually survive solely on ramen noodles. Who knew?

But the reality is if you are only eating “survival foods,” you’ll start feel to sick and weak after a day or two. (Some of these survival foods also have little to zero caloric value, which makes them pointless to eat.)

Oddly, a day or two is about how long it takes to start to feel sick and weak if you don't eat anything at all, with the added benefit of not having worked hard for the feeling.

Myth No. 2: You Can Complete Survival Projects at a Normal Pace

Considering that "a normal pace" for me would make a sloth look like Usain Bolt, I'm not sure this is necessarily true.

The lesson here is on focus. Careful observation of the resources in your environment will dictate what’s possible and what the most important things are to spend your time on. Your decision could be the difference between life and death.

I'd imagine that shelter is of varying importance depending on the climate of where you've gotten yourself lost. A source of fresh water is always of high importance, if you can't find beer.

Myth No. 3: If You Kill a Big-Game Animal, You’re Set for Food

I am the furthest thing from a survivalist that you can possibly imagine, but a moment's thought should be enough to disprove this one. Even if you get past the thought, "Bears," you also have the thought, "This stuff will rot."

But the article doesn't even get into that, talking instead about the danger of trapping animals that don't have much body fat.

Basically, no matter how many rabbits, snails, limpets, or venison stakes you eat, you can still starve to death because your body can’t digest all of that protein without fat.

"Venison stakes?" I think someone killed and ate the editor.

Myth No. 4: Practicing Survival Skills Is the Same as Practicing Survival

This might not be nearly as blindingly obvious as the last one, but it makes sense.

This is a skill that only comes with experience. One indicator that you have this skill is you notice that you’re still having fun in a situation that others are complaining about. Accumulated experience in remote areas lets you know when something like feeling cold, getting cut, or eating something rotten is actually a concern and when it’s not—so you know when to be concerned and when not to be. When you get to this point, it may appear to others that you enjoy misery but you don’t, it’s just that it’s not miserable to you anymore.

And then you can lord it over them with your superior knowledge and attitude. Maybe this will finally make them appreciate you. More likely, you'll find yourself one morning with a cold campfire and no one to practice survival skills with because they've all gone haring off downstream because "obviously, this person can survive on their own."

That's the other thing about survival: we're social creatures; we got to nearly the top of the food chain not by an individual being the best hunter or survivalist, but by supporting each other. One dude can't take down a healthy mammoth alone (without heavy artillery anyway), but a dozen might. Hell, even Thoreau spent a lot of time hanging out with friends while supposedly sequestering himself at Walden (another reason I despise that guy's philosophy: he was a hypocrite).

The ultimate expression of survival is civilization, and that's why I stay near it at all times.

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