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.

December 13, 2021 at 12:02am

#1023146

Congratulations!

For the rest of the month, I may be late posting or, if things don't work out the way I'm expecting, I might miss a day or two. Just a reminder, if you've gotten used to my schedule.

I'll get back to commenting on offsite links tomorrow.

Today, I just want to thank everyone who's been reading, and those who commented yesterday.

⭐Princette♥PengthuluWrites

- 837 day streak here. They say I'm in the top 1%. Your position is even more rarefied. Well done! Félicitations, j'espère que tu continueras.

🌕 HuntersMoon

, 10 years beats my marriage record by a lot. Awesome!

Write_Mikey_Write!

, lots of people wait until the last possible minute to enter a contest. Even people who run contests and challenges. As for the bonus achievement, one advantage of not having a car is I don't run out to fast food places on a whim. Yes, there's Uber Eats, but so far I've resisted.

Sumojo

, the I Write activity is a great motivator, I've found. I know I participated in it once. Can't remember if I finished. I seem to remember getting hung up in September when I just couldn't take another "birthday" prompt. And congrats on the anniversary - you even have 🌕 HuntersMoon

beat there!

QPdoll is Grateful

, that's awesome about the degrees! And obviously I'm a fan of 30DBC, but I don't think I ever participated in all six in one year - that's certainly an achievement.

Lilli 🧿 ☕

, you know, that's a major accomplishment these days.

Leger~

, thanks, always good to hear from you. And waking up every morning is something I've never managed to accomplish, so yay!

Prosperous Snow celebrating

, I tried to do Contest Challenge but I got freaked out at all the backlog. Putting it off is only making it worse. Awesome that you're able to do it. Congrats!

NaNoNette

, I've heard that communication is key to a successful marriage. I wouldn't know firsthand.

Kåre เลียม Enga

, I appreciate all the encouragement you provide, not just to me, but to all bloggers. That's an achievement too. No, I don't feel obligated to write every day. If I did, I'd probably stop because it will have become "work." As long as I want to do it, I'll continue.

And since, like I said, I'm feeling generous, I'll send everyone who commented yesterday a Merit Badge (to be sent out later today). Also, I know I said CR not guaranteed, but if I've sent you one in the past two weeks (I know that applies to a few people here), I will hold off on sending yours until closer to the end of the month.

Again, thanks for reading, and congratulations on all your achievements!

9 Like • Comment • View 4 comments

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