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 2 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.

August 10, 2021 at 12:04am

#1015439

Narcissists

This one's been hanging out in my queue for a while, so I don't really remember the point I was going to illustrate with it; a lot has changed since it was written. But some things haven't, so here it is.

How COVID exposed New Age Narcissism
During this global pandemic that has disrupted life as we know it, many people have attempted to find the silver lining in the chaos

For some, the chaos is the silver lining.

Whatever my original point was, I usually appreciate the perspective of the ex-. That is, someone who used to be an insider and then found a different path. This is one of those stories.

I don't have a lot to quote from it, but it's worth a look.

An example of this paradigm shift is the mass exodus we are seeing away from the “New age/Conscious” community as it currently stands. This article is difficult for me to write, as I have been deeply integrated into this world for over 15 years. Still, like many of you, I have always felt that something was off, although I couldn’t pinpoint it underneath all of the blisstractions.

Ah, that's right... I was going to rag on "blisstractions."

There were a lot of goddesses, warriors, priestesses, and shamans, yet not enough humanity.

Claiming to be one of these things isn't a way to transcend humanity; it's a way to ignore it.

Disinformation and emotional manipulation have always been a part of human history.

In the past, it has convinced white people that Black people are not fully human. It has convinced parents to burn their own children for being witches. And it has sparked up thousands of religions and beliefs that people have been willing to kill and die for. However, due to the Internet, the speed of misinformation and manipulation spreading is at a record high, and humanity needs an Intellectual Renaissance to evolve and survive.

This is something I agree with. Intellectualism has its problems, too, but it's still better than superstition and fear.

You can believe whatever you want to believe, but ultimately, science and truth will prevail.

Unfortunately, by the time they do, it will be too late for us as a society. But hey, it's been a hell of a ride.

Someday, there will be a disease with a much higher mortality rate, which we will not be able to defeat based on how we handled coronavirus. It is easy to forget about the past that we never experienced ourselves. We never saw life before vaccines and medical advancements. But there was a time that a single plague wiped out a whopping 50% to 60% of Europe’s entire population.

I'd just like to point out here that there's an estimate floating around that the diseases the Europeans brought with them to the Americas might have wiped out as much as 90% of the indigenous population, in the 100 years or so between Columbus and Jamestown. Without this unintended biological warfare, the American continent would have a very, very different population right now.

Anyway, like I said: the article's worth a read, even if it says some hard things.

6 Like • Comment • View 5 comments

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