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:

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

December 19, 2020 at 12:01am

#1000467

Got Muffin

"30-Day Blogging Challenge ON HIATUS" [13+]:
19. Oatmeal Muffin Day
Oatmeal is on the healthy side and good for lowering cholesterol.
I feel like I'm being tricked by putting it in an 'unfrosted cupcake'.

"JAFBG" [XGC]:
List 21 things that would make 2021 better than 2020.

Okay, look, I got nothing against oatmeal, muffins, or oatmeal muffins. I don't love them. I don't hate them. Fact is, though, in order to make oatmeal palatable to me, I have to add a bunch of stuff that effectively negates a lot of the health benefits that oatmeal probably has.

A muffin is a bald cupcake.

You know what else lowers cholesterol? A big plate of bacon and a statin.

Anyway. No clever segué today. For anyone following along, I only have two more days of JAFBG prompts, after which I'll do something else. The end of that list coincides with the solstice, so it's a good time for a change.

Only 21 things? There's a large but finite number of "things" that could happen in a year, and it would be challenging to list the opposite: 21 things that would make 2021 worse than 2020. I'm tempted to do it, just because I'm a pessimist like that. Things like: meteor strike, another pandemic that this time turns people into zombies, nuclear holocaust, I personally catch the trump mumps... ummm... maybe that's about it.

A lot of this is, of course, predicated on the idea that things will gradually reopen. I expect they will, at some point. So, in no particular order, only 21 things that would make 2021 better than 2020... for me, which is after all the only thing that matters:

1. Booze.

2. I finally get to go to Europe.

3. Movies in theaters.

4. Restaurants.

5. Road trip!

6. An early spring

7. A new gaming laptop.

8. People stop being stupid (hey, I can dream).

9. No one I care about dies.

10. Visiting breweries and wineries.

11. Getting my deck replaced.

12. New season of Doctor Who.

13. If I manage to get on my arse and edit some stories.

14. Chocolate chip cookies.

15. My HVAC doesn't break down (it'll be paid off in February so I fully expect it to die the day after I make the last payment).

16. If telemarketers somehow lost my mobile number.

17. If I get to meet people in person again.

18. Being able to go to beer festivals.

19. Staying relatively healthy.

20. Not hearing about certain news items anymore.

21. If I don't spend most of the year dealing with a toothache.

All of this reflects more optimism than I'm usually comfortable with. Better to just assume things are going to be worse next year. What's a "year," anyway, but an arbitrarily-bounded orbit of the Earth around the sun? I prefer to begin my new year at a time that's more meaningful to me, like maybe my birthday, which is in February.

We'll see if I make it that long.

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