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 3 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.

September 27, 2020 at 2:27am

#994334

Not So Prompt

Oh, yeah! Hung-over prompts time!

PROMPT September 27th

We are nearing the end of the month, and as always, I need your help to fill the Challenge War Chest with new prompts! In your entry today, write three of your own blogging prompts and then use one of them to complete your entry.

So, let's see. Blog prompts. Many of this month's prompts have been quite thought-provoking, and I'm not sure I can top them in my current condition. Fortunately, I don't have to top them, just come up with different ones.

In that spirit...

1) What are your favorite procrastination techniques?

2) Tell us about your favorite food. Include all the sensory description you can: smell, sight, etc. Why do you eat it even though you know it's bad for you?

3) Talk about a time someone gave you a compliment, but you felt you didn't deserve it.

Yeah, I know, they're kinda salty. If you had my hangover right now you'd be pickled too.

Because this entry is later than my usual entries, I figure it's appropriate to tackle #1.

What are your favorite procrastination techniques?

Oh, there are so many. So, so many.

I guess the most important procrastination technique is "forgetfulness." When I know I have something important to do by a deadline, I distract myself by doing something else until I forget what it is or when it's due. Then I wake up in the middle of the night screaming because I suddenly remember what it was, how essential it was for my well-being, and that it was due last week.

Another good one is cleaning. Now, I hate cleaning with an all-consuming passion, but occasionally I get saddled with something I want to do even less. This is a good way to actually get me to straighten some things up, because I tell myself cleaning doesn't require a lot of brain power and I can use the time to think about the thing whose deadline is rapidly approaching. Usually this means I half-ass the cleaning and half-ass the... whatever the other project is.

Then there are the times I convince myself that in order to do project A, first I need to tackle project B. But project B requires the results of project C, which in turn requires me to complete project D. The biggest problem here is that project D is heavily dependent on project A being complete. I call this Recursion to Infinity Procrastination, or RIP, which will be etched on the tombstones of my unfinished projects.

Occasionally, procrastination isn't all bad, and I manage to get other things done, like when I'm stuck on a story so I decide to do some reviewing instead. At least then I get reviews done. Most of the time, though, I just waste time until the adrenaline kicks in so I can't wait any longer.

If you're expecting me to be all sunshine and light here and give tips for not procrastinating, remember 1) who you're reading here and 2) the hangover bit from above.

Hopefully, though, this has been at least a teensy bit amusing for you readers, because I'm suffering for my art here, and my art is supposed to be comedy.

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