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 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 12, 2022 at 12:02am

#1036403

So Low

Sometimes, I can relate to the things I share here.

This is not one of those times.

How I Learned to Eat Alone and Not Be Lonely
What two years of solo dinners taught me

You just... eat. That's how.

But I guess that's not enough for extroverts.

In the spring of 2020, as my world shrunk to the square footage of my apartment, food became a mode of injecting pleasure and delight into an otherwise bleak and lonely period of my life.

Oh great. A pandemic whine.

As time passed, I wondered when, or if, I’d get to dine with friends and family again. I entered a state of despair.

Don't get me wrong. I enjoy sharing meals with friends and family. But for me, the despair would be if I didn't know when I'd get to eat alone again.

I relied on books, Netflix, and even work to distract myself at dinner.

The horror.

Eventually I downloaded TikTok, and then that became my new dining companion.

The horror! (This time it's not meant sarcastically.)

I began seeing myself mirrored on my “For You” page, which served up videos of other people eating alone. In the videos, creators talked to their presumed audiences in animated voices: “I’m so proud of you for eating today,” “No matter what, you deserve to nourish your body,” or “I’m going to take a bite, and then you take one.” Why were these people filming an ordinary, solitary experience and sharing it online? And why were millions of strangers, myself included, watching them every night?

At this point, I got the feeling that even if the article answered those questions, I still wouldn't comprehend. How do you go about "not eating?" My entire day, no matter what else I'm doing, is taken up with one of four things: Preparing food, eating food, thinking about the next meal, and, while sleeping, dreaming about food.

Even if I decide something like, "I need to not eat for the next twelve hours," I'm still thinking about what breakfast will be.

Many of these videos are designed to encourage viewers, especially those with eating disorders or mental-health diagnoses, to eat in tandem with the creator.

Okay. Okay, I can accept that some people have mental health issues about it. By no means am I trying to minimize those; I have my own, different issues. But, as with people who are gay or who enjoy anchovies on pizza, I can't fully understand; I can only accept.

They found me, in the strange way that the TikTok algorithm knows you better than you know yourself.

Which, right there, is enough reason for me to avoid that platform like poverty. ("Like the plague" is overused, clichéd, and it turns out people don't avoid that.)

One account that I visited frequently was @foodwithsoy, run by Soy Nguyen, a food influencer based in Los Angeles.

I did have a nice laugh at that aptronym, until I got to the "influencer" part and nearly puked.

It would be pronounced like "Soy Win."

The videos can also balance out messages pushing diet culture and weight loss, says Jaime Sidani, an assistant professor of public health at the University of Pittsburgh. There are real concerns that apps like TikTok can serve as a conduit for harmful eating behavior and poor body image.

Okay, so... that much I can appreciate.

In conclusion, while I felt no affinity to the article, I'm posting it here in the hopes that it might help someone else. Unless you're already using DikTok, in which case there's no hope for you.

4 Like • Comment • View 4 comments

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