Complex Numbers (Book)

Blog Calendar

◄ May ►
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	31
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:

Adherennium Plotting something

about 2 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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

May 24, 2024 at 7:04am

#1071617

Plan Solo

As I normally travel alone, today's article seemed relevant to my interests. (Source is Condé Nast Traveller, if it matters.)

The golden rules of solo travel
We ask our editors and favourite solo travellers for their savviest tips and tricks

Apparently, there's a US and UK version of that outlet. The spelling gives away that it's from the latter. But as it's about travel, I don't think the country of origin matters much.

The joys of travelling solo are endless.

I wouldn't say "endless." Just "ending later than if you have someone with you to eventually argue with."

There is something truly freeing about exploring new places alone – you can go where you please, eat when you want, and have uninterrupted quality time with yourself.

No sleep-shaming, no pressure to fit too many things into one day, no bargaining about "If we do X today, I want to do Y tomorrow," etc.

The interest in solo travel has been slowly rising for a while, but new data from UK-based travel organisation ABTA shows that 16 per cent of travellers went on holiday by themselves in 2023, a five per cent increase from the previous 12-month period.

I wonder if there had been a global problem that made people tired of always seeing the same other people all the time.

But, if you’re not a seasoned solo traveller, it can be a daunting prospect. In an age of constant connectivity, the idea of being alone for an extended period of time is a convoluted one.

The only way I'd be "alone for an extended period of time" would be if I went hiking by myself in the wilderness, which is not only a bad idea to begin with (though I've done it), but it would involve being *shudder* outdoors.

Below, we spoke to travellers who frequently book solo trips about their golden rules for travelling alone.

"Rules?" Hey, I travel alone so no one gives me "rules."

Dining alone isn’t weird
For most people, the thought of dining alone is one of the biggest barriers to travelling solo.

Yeah, I just can't relate to that. If I'm alone, I can focus on the things that really matter: the dining and drinking experience. Besides, no one is there to tell me they just can't stand whatever cuisine I've decided to try.

Fake it til you make it
Most people feel nervous about meeting new people, and introverts especially can struggle to make the first move when arriving in a new place.

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

Book counter dining at restaurants
If you are someone who does feel uncomfortable about dining alone, opt for a bar or counter seat.

While I don't travel internationally as much as I'd like, here in the US at least, the bar usually doesn't require reservations or other planning ahead, apart from maybe figuring out a time to go when it's not too crowded.

Plan around cultural events
Arriving at a destination just as the locals are gearing up for an important cultural event can be an incredible way to immerse yourself straight away.

It's also an incredible way to have everything crowded and sold out. Hell no. Give me off-peak travel any day.

Exception: my desire to visit Scotland during the Islay Festival for the best whiskey in the world.

Build in group activities
Booking tours and group events is a great way to meet other travellers. Most hostels have a list of activities available for guests to sign up for, and if not, then there are walking tours or live music events at local bars.

Honestly, I'm torn about this bit, personally. First of all, I'm not interested in hostels, but let's leave that aside for now. And while I love music and bars, I despise music events at bars, because I can't hear the bartender.

My passport expires in 2026. I've never used this incarnation of it, because, well, you know. I want to use it at least once, and I don't mean crossing the border into Canada. As the person I was planning to go to Belgium with has other priorities now, I'll be going alone, which is fine. Maybe France, first, though... but not until after the Olympics (see above re: crowds).

Now I just have to get on my ass and make the plans.

2 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.