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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day 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

Nov 14, 2024 at 12:10pm
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').

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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

January 16, 2019 at 12:29am

#949749

Can't Stress Enough

I have a stressful day at work today ... What strategies do you use to manage stress in your life?

Honestly, the strategies I use to manage stress in my life wouldn't work for most people. They include:

Going to sleep when I want to and waking up whenever it happens naturally

Not having kids

Not having a job

Avoiding stressful situations

Drinking

Staying away from people who want to tell me how I should live

Since we're on that last subject, I did come across this list,

which had the opposite effect of its clear intention, as reading it made my blood boil.

It's titled "50 Ways To Live On Your Own Terms," but it should be titled "50 Ways To Live On My Terms Because I'm Better Than You."

While there are a few - very few! - points on this list with which I agree, it started to piss me off from #1.

1. Stop consuming caffeine

How about you bite me?

And then there's:

2. Pray or meditate morning, mid-day, and night

Okay, let's think about the normal American life for a minute.

You have 24 hours in a day. No more, no less (okay, with the possible exception of two days a year when you switch from DST or back, but let's not be too pedantic about it).

Everyone who has an opinion about it, including the author of this drivel, recommends 8 hours of sleep. That leaves 16.

You work for 8 hours a day. That leaves 8.

A normal commute is 1 hour. That's 2 hours, leaving 6.

Waking up, showering, getting dressed, eating breakfast - let's be generous and call it 0.5. Leaves 5.5.

Lunch. Usually an hour. Leaves 4.5.

Doing stuff to get ready for bed. Another half-hour. Leaves 4 hours.

Exercise. I'll grudgingly admit that exercise is good for you. You should do that every day. Even if your routine is only 1/2 hour long, which I take to be a minimum, you also need time to go to the gym, get dressed, get dressed again, and come back from the gym. Call it another 1/2 hour. If you're only exercising for 1/2 hour like I said, we're down to 3 hours.

Dinner. Maybe you have someone to cook it for you; maybe you're doing the cooking. If you're doing it, between cooking, cleaning up, and actually eating, that's easily an hour. Now we have 2 hours left in the day.

What am I missing? Oh yeah, sex. To do it right takes at least an hour. Feel free to make jokes about it only taking 30 seconds in the comments. But I stand by my math here.

So, let's see, carry the 2... you have one hour to do other stuff, and that's if you don't have kids.

Now, sure, you can, for instance, order a pizza instead of cooking dinner and free up some time that way, but we're talking about trying to lead a healthy lifestyle here, right? Personally, I'd order the pizza, but we all know I'm no role model.

Or maybe you can enrich yourself by listening to an audiobook whilst commuting or at the gym. Still, if you remember, this entire section of the rant is about squeezing in meditation time, and for that you need to be mindful, focused, and undistracted by other stuff.

Something usually gives. For me, it was sleep. I'm still feeling the negative effects of that. Don't be me.

Point is, we're only on #2 and I've already explained why the list is full of shit.

Now, I'm not going to go into all of these. You can read the mishigoss for yourself and draw your own conclusions. They might be different than mine. That's fine. But here are a few other lowlights:

13. Go to bed early and rise early

Let me explain this one more time: Some people have different natural schedules. If you're getting the recommended 8 hours of sleep a day (which you're not), what the fuck does it matter what the clock says when you're doing it?

There might be a correlation between natural morning people and productivity. But correlation != causation.

15. Replace warm showers with cold ones

Bugger off, wanker. Of all the simple pleasures in life, this is the only one that has no godsdamned calories or carcinogens.

23. Replaces Carbs With Healthy Fats

There’s lots of research showing that healthy fats don’t make you fat. Actually, refined carbs and sugars are what make you fat.

Actually, calories are what make you fat. Refined carbs and sugars make you hungry faster, so if you're undisciplined (like me), you end up eating more calories overall.

And you know how I feel about nutritional "research." I won't go into it again here.

25. Choose to have faith in something bigger than yourself, skepticism is easy

I find that the precise, exact, polar opposite is true. Atheists make up a small percentage of the population, and most of us arrived at that philosophical point after a lot of hard thinking and self-searching, and with resistance from almost everyone else in our lives. If you think being a minority is easy, you're not a minority.

27. Give at least one guilt-free hour to relaxation per day

Aaaaaand there goes your final hour.

43. Make your bed first thing in the morning

Making your bed is an utter, complete, and total waste of time.

47. Become good friends with your parents

Go to hell. My parents each spent 10 years struggling with dementia, then died. Not even concurrently. I spent 20 years of my life dealing with that. You know, in case you wanted to know why I'm so angry sometimes.

Now, I could also mention the few items I can agree with, but what's the point? The rest of the article calls those into question for me, so I'm going to spend the next couple of weeks reevaluating, for example, 48. Floss your teeth.

Hey, look at that, I was supposed to write about dealing with stress, and instead, I managed to cause some.

I want a drink.

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