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 6 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 8 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.

July 17, 2021 at 12:04am

#1013786

Indulge Me

Only halfway through "JAFBG"

[XGC]...

Sometimes we have to tell the world to fuck off and just look after number one. What do you do (or wish you could do) for self-care?

Are you kidding me? I've arranged my life around not having to do more than the bare minimum for other people.

When you're single, retired, and don't have kids, you can do that. I know for some that would be a meaningless existence, but existence is meaningless anyway, so what's the difference?

Nevertheless, I don't know what self-care is supposed to be. I guess you can count sleeping. I'm a big fan of waking up whenever the hell I please, not being constrained by alarms. Of course, the world being what it is, sometimes you have to get up at a certain time; that's just life. And when I travel, I do try to be awake for experiences. Sometimes I'll even wake up for the sunrise, instead of staying up for it.

But sleep is important to me. It's not optional, and it's not generally something that can go by the wayside so I can do other stuff. Interfere with my sleep cycle at your peril. There had better be a fire or flood, and, moreover, something I can do about the emergency besides wait for impending doom. I'd rather die in my sleep.

Still. This isn't meant to imply that I don't care about other people. Or my cats. I try to fulfill my responsibilities; it's just that I work hard to avoid having too many responsibilities in the first place.

I understand that for some people, I don't know how many, it's in the gathering and discharge of responsibilities that they find self-actualization. But not everyone is like that. If you try to impose that on someone like me, it just becomes frustrating, aggravating, infuriating, or worse, like forcing an introvert to be an extrovert, or a night person to be a morning person.

I've known people who live only for others. Some of them do just fine with it. Others... well, others could use a good night's sleep, or a bong hit, or a nice tall cold beer. One of the greatest lies perpetrated on us is that self-indulgence is always wrong. Certainly, too much can be detrimental -- but then it ceases to be self-care and just becomes self-destruction.

After all, if you don't take care of yourself, how can you take care of others?

The trick is finding the balance, and that point will be different for everyone.

Still, moderation only works in moderation. Sometimes you have to go for excess.

Speaking of self-indulgence, on Thursday, I went to see Black Widow, and then I completely forgot to review it here. So I'm doing it now.

One-Sentence Movie Review: Black Widow

While you will need to have some familiarity with the Marvel Cinematic Universe to fully understand some of the references in the movie, there are enough gun battles, fight scenes, car chases, explosions, and special effects to make the film shine on its own, along with an actual plot with a satisfying mix of humor and drama; many of the scenes are unrealistic, but come on, it's an action/adventure science fiction movie based on comic book characters, so no one should go into this movie expecting adherence to the rules of physics or biology, just the Rule of Cool.

Rating: 4/5

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