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 15 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 17 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.

April 6, 2020 at 12:03am

#980351

Does Whatever A Spider Can

How about some love for our cuddly, eight-legged friends?

https://theconversation.com/should-i-kill-spiders-in-my-home-an-entomologist-exp...

Should I kill spiders in my home? An entomologist explains why not to

I know it may be hard to convince you, but let me try: Don’t kill the next spider you see in your home.

Of course not! Make your partner do it.

Why? Because spiders are an important part of nature and our indoor ecosystem – as well as being fellow organisms in their own right.

Poison ivy is a "fellow organism" too. Argument fails.

Some species even enjoy the great indoors, where they happily live out their lives and make more spiders.

Usually right above your bed.

And they may be providing services like eating pests – some even eat other spiders.

But other spiders are fellow organisms in their own right!

My colleagues and I conducted a visual survey of 50 North Carolina homes to inventory just which arthropods live under our roofs. Every single house we visited was home to spiders.

Whew! Fortunately, I live in Virginia.

Although they are generalist predators, apt to eat anything they can catch, spiders regularly capture nuisance pests and even disease-carrying insects – for example, mosquitoes.

But mosquitoes are fellow orga- you know what, I can't keep typing this with a straight face.

But if you can stomach it, it’s OK to have spiders in your home. In fact, it’s normal. And frankly, even if you don’t see them, they’ll still be there. So consider a live-and-let-live approach to the next spider you encounter.

That's hard to do when you swallow dozens of them in your sleep, or when they crawl into your nose and die in your snot, or...

Okay, the sleep-eating thing is false. Not sure about the nose thing.

But seriously, though, I'm not an arachnophobe; I just like messing with those who are. Spiders and I have an arrangement. Outside spiders are my friends. I've had them build webs around my deck and I love watching them. Inside spiders stay out of sight, or they become outside spiders.

I'd probably feel different about it if I lived in Australia, where rumor has it their chief prey is kangaroo. And when suddenly confronted with a huge fucking spider, I channel my inner little girl just like everyone else who is sane. But once I get over the initial reaction, they really are kind of cool.

6 Like • Comment • View 10 comments

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