Complex Numbers (Book)

Blog Calendar

◄ October ► 2023
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:

QPdoll

about 11 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

about 14 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

October 26, 2023 at 10:06am

#1058097

The Dark Side

I put up with reading articles like this one only so I can rag on them.

If You Want To Be Truly Free And Happy, You Must Banish These 4 Thoughts
Nothing good will happen to you if you're negative all the time.

And already I'm negative about it.

Are you clinging to something that is not serving you?

My cats, for some reason, refuse to serve me; they insist that the other way around is the natural order of things.

Do you feel doubt? Failure? Depressed?

Are you about to tell me that I can think my way out of clinical depression?

It’s time to let go of negativity and pain and accept life as it is.

Ha, ha, very funny.

...oh, wait. You're serious.

We encounter numerous toxic people every day who deliver subtle negative messages and instill negative ideas constantly.

And so we come to the root of why they want us to banish the negative and plaster smiles on our faces and pretend everything's sunshine and peaches: being a grump inconveniences other people.

However, in order to cultivate a positive mindset, you need to develop a strong mentality and separate yourself from the general crowd.

Once you do those things, you won't need to cultivate a positive mindset. Life will automatically be less stressful.

By giving more power to negativity, you will send out negative thoughts to the universe and end up attracting and manifesting negative things only.

Ah, yes, the power of magical thinking. Kind of the opposite of "develop a strong mentality" here.

If you let negativity creep into your mind, it will steal all your peace and happiness and put you in a dark pit of suffering.

Follow Master Yoda you must. Heed his words you should. "Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering."

To be clear here, I work to live my life without fear, anger, or hate. If those are the "negative" things they want banished, well, you're never going to banish them entirely, not without giving up everything that's worthwhile in the process. But that doesn't mean you have to let these things control you.

Shift your focus to the positive aspects of life, as there is always a silver lining in even the darkest situations.

Conversely, there's always a dark cloud in even the brightest situations.

Your reality is not based on what others think or say about you.

Neither does it depend on your negative thoughts or self-doubt.

... but you just said that it did, that negative thoughts manifest themselves through the universe's karmic channels or whatever. Which is it? (Answer: neither. Reality includes your thoughts, but is independent of your thoughts. Perception, sure. But not reality.)

So start by letting go of negative perspectives, grudges, jealousy, fear, pain, self-doubt, and toxic relationships that might hold you back.

I could take these one by one, but I have a dentist appointment later this morning, so I have limited time. While I tentatively agree that a lot of those things stunt one's personal growth, a healthy dose of self-doubt is important to keep a person from being too arrogant. And don't get me started on "pain." Assuming that means mental anguish and not physical pain, first, it's not so easy to get past trauma, and second, sometimes you have to wallow in it for a while before you get better.

When you let go of negativity from your past, you will be more mindful and bring your awareness to the present moment and stop worrying about what you cannot control.

I'm all for not worrying about what you can't control, but screw this "present moment" and "mindfulness" bullshit. We're nothing without our pasts, and if we don't concern ourselves with the future, it'll smack us in the faces.

Here are a few proven ways to help you release negativity from your life.

"Proven?" [citation needed]

I won't go into the "few ways." The article is there if you want to draw your own conclusions.

I'm not even saying everything in the article is wrong. As I said above, I'm not a fan of letting anger control me, and I don't live my life in fear. But there's also a hefty dose of airy nonsense and denial of reality, or at least a lack of acknowledgement thereof. Banish anger completely, and there goes one motivation to make positive changes. Banish fear, and you might think it's okay to take that shortcut through Mugger Alley.

Perhaps getting stuck in Pollyanna world is preferable to getting stuck in Eeyore world. But I'd rather not get stuck anywhere.

6 Like • Comment • View 2 comments

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