Complex Numbers (Book)

Blog Calendar

◄ June ► 2019
S	M	T	W	T	F	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

a day 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

a day 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.

June 18, 2019 at 12:37am

#960971

Heartbreak

https://www.bbc.com/news/health-47440622

Your heart can be damaged after a sad event and it may be your brain's doing, experts believe.

Teen angst, vindicated!

Dr Jelena Ghadri and colleagues at University Hospital Zurich looked at what was happening in the brains of 15 patients with broken heart syndrome.

Brain scans showed up noticeable differences compared with scans from 39 healthy, control patients.

There was less communication between brain regions involved with controlling emotions and unconscious or automatic body responses, such as heartbeat.

The more I learn, the more I think that the commonly stated dichotomy between mind and body is bogus.

It started with my mother. (Cue Sigmund Freud.)

Mom was diagnosed with ulcerative colitis before I was born. They treated her for that for decades. And then another doctor looked at her and said, "It's not ulcerative colitis; it's Krohn's Disease."

As I understand it, they present with similar symptoms, but the treatment is different. But it was too late for her; she'd been damaged.

Why is this relevant? Because it also affected her mind. Maybe it was the stress of living with a difficult condition, or maybe it was the treatments, or perhaps a combination, but as she grew older, she just wasn't right in the head. Eventually, this led to dementia and her ultimate death.

Now, today, I just read that scientists are investigating a possible connection between streptococcus infections and certain types of mental illness. And then, of course, there's this.

And yet, people continue to treat mind as something separate from the physical. I know it certainly seems that way sometimes, but to me, what goes on in one's brain is undoubtedly influenced by what's going on in the body. The reverse is more clearly true, but it's rather obvious that chemical and electrical processes can influence one's thoughts just as surely as they can damage organs or make changes in one's body - adrenaline prodding muscles into action, for example.

Anyway, back to the actual article I linked.

Dr Ghadri said: "Emotions are processed in the brain so it is conceivable that the disease originates in the brain with top-down influences on the heart."

The idea of the heart as the seat of the emotions is ubiquitous in our culture. It predates the advent of modern medicine. There's some poetry in that - every cliché starts is life as profound poetry - but it's clear that, from a purely medical standpoint, it's all in one's head. And yet, according to this study at least, there's a connection there; everything in the body is interconnected.

I'm far from an expert at medical matters, and even farther from an expert at issues of emotion. So, really, I don't know how to interpret all of this. It's just something to think about - if you can stomach it.

Consequently, I'll just post the literal video version of Total Eclipse of the Heart.

6 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.