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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 14 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 16 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 3, 2022 at 12:02am

#1029962

Plowadise

This one's been hanging around in my queue for a while, and some might say it's a bit outdated, as it involves the names of snowplows. Anyone who thinks it's the wrong season, however, is obviously not familiar with Michigan.

MDOT Snowplow Names

Now, some of these are kind of plain, like Blue Water Express and Snow Captain. And some I'm sure you could have thought of yourself. But there were a few that had me howling. And others that are questionable at best.

Auntie Arctica

Okay, look, this is a prime example of unnecessary complication. Maybe it's a Michigan thing (confession: it's one of only three stats I haven't actually been to). But why not simply Aunt Arctica? No one actually pronounces it Ont anymore, so Aunt Arctica is a great pun.

Baby Snowda

One of many Star Wars-themed names. When a juvenile of Yoda's species (whatever that is) was introduced in The Mandalorian as a transparent attempt to get people talking about the show on social media -- hey look it's a cute thing with big eyes; we've never seen that from Disney before -- his name was unknown at first, so everyone started calling him Baby Yoda.

But, as his actual name is Grogu, why not Snowgu?

Heikki Lunta

Someone's gonna have to explain this one to me.

Sleetwood Mac

Remember the other day I was talking about making up band names? Yeah.

The Big LePlowski

Obviously, this one is one of my favorites.

Snowbegone Kenobi

This Star Wars reference is really quite clever.

Yooper Scooper

Clever, funny, but I'm pretty sure it reflects how Lower Michigan actually feels about the Upper Peninsula.

Blade Runner

Finally, a movie reference that doesn't require a pun.

S'no Problem
It's Snow Problem

...really?

Plowthagorean Theorem

This one can only move on the diagonal, I assume.

Sir Plows-A-Lot

Okay, look, riffs on Lancelot are lamer than puns about the seventh planet from the sun. Stop it.

Snowcrusher

What? No Snowpiercer?

The Kraken

No, no, he lives in Minnesota, not Michigan.

Dolly Plowton

Please tell me that one has bigger headlights than the others.

Lake Scooperior

I gotta give 'em props for this one.

Saul T. Streets

Groan.

And finally, the most Michigan possible name for a snowplow:

Still Shorts Weather

There are a lot more at the link, so go take a look.

3 Like • Comment • View 3 comments

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