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 5 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 5, 2021 at 12:01am

#1007766

Procrasti-later

Here's another one for all my fellow procrastinators out there. I keep meaning to get a procrastinators' convention together, but can't ever seem to get around to it.

'Why Do I Spend Weeks Avoiding Tasks That Will Take Me 10 Minutes to Do?'
Procrastinating has less to do with time management and more to do with mood management.

The article is dated from mid-January and I'm just now posting it.

Sometimes we just can’t make ourselves do stuff! Last month, when I asked people to talk about times they’d opted to not do something that they could also simply… do… my mentions were flooded.

Example: taxes. Here in the US, the Federal income tax deadline is usually April 15, though it's been extended this year due to... you know. Individual states, the ones that have state taxes, have different deadlines. Either way, it needs to be done soon. My accountant has been bugging me, and I've collected most of what I need. The rest? Well. I'll get to it eventually.

I can't tell you how many times I've mentally prodded myself to Just Do The Thing and yet fail to do that very thing. Until it's the last minute. Or after. Blogging every day has helped a little bit with that, but the underlying problem (me) remains.

Whether it’s watching your plants wither for weeks before repotting them (total time to complete: six minutes) or waiting until you get pulled over to replace the registration sticker that’s been expired for a year (that was me, I did this), a lot of folks are procrastinating on alllll kinds of little things.

How about procrastinating on getting someone to edit your article?

Why, exactly? When it’s relatively simple to Do The Thing, and when the consequences of Not Doing The Thing can be serious or fairly unpleasant, why do so many of us look the other way?

Of course the article goes on to answer that question. It's a Vice article, not clickbait. Oh, wait...

“We get punished for being late in our culture,” Ferrari said. “We don’t get rewarded for being early.” And when you internalize the message that there’s no point in being early, you can apply that to any task that needs doing.

Well, that's just a matter of point of view, isn't it? If you're a procrastinator, things are often late and you suffer negative consequences. These consequences comprise your default. So anything better than the default is a reward, such as not suffering negative consequences. That's the same thing as a reward in my book.

“Procrastination is an avoidant way of coping,” Sirois said. “How do I manage uncomfortable feelings around that paperwork I have to do? I know, I’ll put the task aside and feel better about it. Ah, I feel better already. You just managed your mood by procrastinating.”

This makes sense. To go back to the taxes thing, I always end up owing money. I do not want to pay money. So I put it off. Which sometimes means I owe more money.

That fear of fucking up can keep you from starting in the first place—even if it’s a little thing like taking five seconds to write a text or answer an email. And on the other hand, if you do a good job... well, what if you can’t maintain it? What if you can’t do it as well the next time?

Which may explain at least one reason I haven't really pursued story publication.

Procrastination tends to be a solitary struggle, but literally everyone does it!

I know people who don't. Stop misusing "literally."

And if this behavior has become a regular occurrence—the kind of thing that’s paralyzing you in your personal and professional life or preventing you from reaching your goals—it might be time to talk to a professional. Chronic procrastination can be a symptom of anxiety disorders, depression, and ADHD; a mental health expert will be able to tell you more.

I've had a shrink's number pasted on my board since December. Have I called them yet? What do you think?

2 Like • Comment • View 4 comments

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