What are Complex Numbers and Why Do They Matter at 13 Years Old?

[Dashin]

(No, I'm not 13!, I'm 13. I am not THAT old)

Hi! I'm not sure where to put a "Hello" message, so I suppose here will do. Great to be here.

Before you think "GTFO 13 year old", I love Complex Numbers (I prefer "Complex" to "Imaginary" because "REAL" numbers are actually figments of our imagination also) and I also love the satisfying answer of e^(pi*i)=-1, and the way it works.

So, um, yeah. Not sure what else to say here. I'm a bit of a Math Nazi when it comes to rounding, in that I hate to do it. "A Ball Falls to the Ground at accelleration of 10 Newtons per second"... It falls at 9.81 (still roughly), not 10.

So... Um... Great to be on a forum with smart people for once.

~ Dashin

EDIT: Great, a math Nazi. I'm actually 13.490303762009785, not 13.

 

[Hobin]

(No, I'm not 13!, I'm 13. I am not THAT old)

Given that you didn't provide a unit of measurement, it sort of works if you are 13! in 1/15*seconds.

Hi! I'm not sure where to put a "Hello" message, so I suppose here will do. Great to be here.

Welcome to PF! Incidentally, what's your favourite fish?

So, um, yeah. Not sure what else to say here. I'm a bit of a Math Nazi when it comes to rounding, in that I hate to do it. "A Ball Falls to the Ground at accelleration of 10 Newtons per second"... It falls at 9.81 (still roughly), not 10.

Ahem. Thou shalt keep significant figures in mind, or risk the wrath of the physicists.

So... Um... Great to be on a forum with smart people for once.

Heh. You're only *supposed* to think that. Most of us are just insane. Shhh, don't tell anyone.

 

[Jimmy Snyder]

Happy birthday Dashin.

 

[Dashin]

Given that you didn't provide a unit of measurement, it sort of works if you are 13! in 1/15*seconds.

*facehoof* I was being rough, and I meant YEARS old. And... *facehoof*

Welcome to PF! Incidentally, what's your favourite fish?

Cod.

Ahem. Thou shalt keep significant figures in mind, or risk the wrath of the physicists.

Lolok

Heh. You're only *supposed* to think that. Most of us are just insane. Shhh, don't tell anyone.

Uh, Okay.

Happy birthday Dashin.

xD
I'm ACTUALLY 13.490303762009785

 

[chiro]

(No, I'm not 13!, I'm 13. I am not THAT old)

Hi! I'm not sure where to put a "Hello" message, so I suppose here will do. Great to be here.

Before you think "GTFO 13 year old", I love Complex Numbers (I prefer "Complex" to "Imaginary" because "REAL" numbers are actually figments of our imagination also) and I also love the satisfying answer of e^(pi*i)=-1, and the way it works.

So, um, yeah. Not sure what else to say here. I'm a bit of a Math Nazi when it comes to rounding, in that I hate to do it. "A Ball Falls to the Ground at accelleration of 10 Newtons per second"... It falls at 9.81 (still roughly), not 10.

So... Um... Great to be on a forum with smart people for once.

~ Dashin

EDIT: Great, a math Nazi. I'm actually 13.490303762009785, not 13.

Welcome to the forums Dashin.

I hope you enjoy your time here and I hope you get a lot out of these forums: I like many others here, do on a regular basis: it's a great community :)

 

[Dashin]

Welcome to the forums Dashin.

I hope you enjoy your time here and I hope you get a lot out of these forums: I like many others here, do on a regular basis: it's a great community :)

It seems like a great community - I got asked about fish.

 

[chiro]

It seems like a great community - I got asked about fish.

Yeah don't worry about that, those guys are nuts ;)

If you are curious its a weird initiation rite here kind like an induction ceremony into a tribe kinda thing.

 

[Mépris]

Good to have you on board, young Sir.

I see you're from the UK. Did you skip a few grades to A-Level Maths or is your knowledge of complex numbers and kinematics a result of independent study? In any case, kudos to you. :-)

 

[Dashin]

Yeah don't worry about that, those guys are nuts ;)

If you are curious its a weird initiation rite here kind like an induction ceremony into a tribe kinda thing.

Uhm, Okay? Did I answer correctly?

 

[chiro]

Uhm, Okay? Did I answer correctly?

Yeah dude you're fine: your not a witch and we won't burn you at the stake ;)

 

[Dashin]

Yeah dude you're fine: your not a witch and we won't burn you at the stake ;)

Yeaaaah... this is totally to do with Math...

 

[Hobin]

Yeaaaah... this is totally to do with Math...

*slaps Dashin with a big, fat, codfish*

http://files.myopera.com/Chyren/files/fishSlap1a.gif

Now you're officially one of us. Welcome to the PF cult.

 

[arildno]

Hi, Dashin!
Rounding numbers are often the most sensible thing to do, bevause keeping "too many" digits falsely imply a higher degree of accuracy to measured numbers than you actually have.

Suppose you have to measured numbers 3.7 and 4.3. Your measuring tool is not good enough to distinguish between numbers lying between 3.65 and 3.75, and "3.7" is your measured number for the possible INTERVAL of numbers 3.65 to 3.75. We say you know the "number" to two significant digits, in this case.

Simliarly, "4.3" stands for any number within the interval 4.25 to 4.35, and we know the "true" number to two significant digits as well.

When you multiply, for example, 3.7*4.3=15.91, you are to round this off to..two significant digits, i.e, give the answer as..16

Why?

Consider the HIGHEST product the two number intervals could produce, i.e 3.75*4.35=16.3125

The LOWEST number that interval can produce through multiplication is 3.65*4.25=15.5125

Thus, your "exact" answer, 15.91 gives the FALSE IMPRESSION that your product must lie between 15.905 and 15.915

Instead, keeping the answer to two significant digits, i.e rounding 15.91 to 16, then you are saying the "true" answer must lie between..15.5 and 16.5, which is absolutely..TRUE!

THAT is the real importance of rounding, not to introduce a false level of accuracy in your answers for inexactly measured numbers.
---
The best thumb rule is:
You are to round off your answers to the least number of significant digits in the measured numbers you do algebraic operations on.

 

[Dashin]

Hi, Dashin!
Rounding numbers are often the most sensible thing to do, bevause keeping "too many" digits falsely imply a higher degree of accuracy to measured numbers than you actually have.

Suppose you have to measured numbers 3.7 and 4.3. Your measuring tool is not good enough to distinguish between numbers lying between 3.65 and 3.75, and "3.7" is your measured number for the possible INTERVAL of numbers 3.65 to 3.75. We say you know the "number" to two significant digits, in this case.

Simliarly, "4.3" stands for any number within the interval 4.25 to 4.35, and we know the "true" number to two significant digits as well.

When you multiply, for example, 3.7*4.3=15.91, you are to round this off to..two significant digits, i.e, give the answer as..16

Why?

Consider the HIGHEST product the two number intervals could produce, i.e 3.75*4.35=16.3125

The LOWEST number that interval can produce through multiplication is 3.65*4.25=15.5125

Thus, your "exact" answer, 15.91 gives the FALSE IMPRESSION that your product must lie between 15.905 and 15.915

Instead, keeping the answer to two significant digits, i.e rounding 15.91 to 16, then you are saying the "true" answer must lie between..15.5 and 16.5, which is absolutely..TRUE!

THAT is the real importance of rounding, not to introduce a false level of accuracy in your answers for inexactly measured numbers.
---
The best thumb rule is:
You are to round off your answers to the least number of significant digits in the measured numbers you do algebraic operations on.

Oh yeah, obviously for measurements xD

 

[arildno]

And isn't 9.81 a measurement?
Suppose you have given the mass of an object to one significant digit, say 2kg.
If you are to estimate the gravitational FORCE acting upon the object, it is meaningless to keep the acceleration due to gravity at 9.81, but round it off to one significant digit, i.e, 10 (ending zeroes are NOT significant digits).

Thus, the force upon the object will be 20 N, to one significant digit's accuracy, i.e, the EXACT force lying somewhere between 25N and 15N

 

[Jimmy Snyder]

Oh yeah, obviously for measurements xD

But not for e or \pi?

 

[Dashin]

And isn't 9.81 a measurement?
Suppose you have given the mass of an object to one significant digit, say 2kg.
If you are to estimate the gravitational FORCE acting upon the object, it is meaningless to keep the acceleration due to gravity at 9.81, but round it off to one significant digit, i.e, 10 (ending zeroes are NOT significant digits).

Thus, the force upon the object will be 20 N, to one significant digit's accuracy, i.e, the EXACT force lying somewhere between 25N and 15N

*le shrug*
Fair enough.

But not for e or \pi?

I will use as many digits as possible for e or Pi. (obviously no more than 40 for Pi - the amount needed for atoms spanning universe)

 

[arildno]

*le shrug*
Fair enough.
I will use as many digits as possible for e or Pi. (obviously no more than 40 for Pi - the amount needed for atoms spanning universe)

isn't "e" the exact value of..."e"?

 

[Dashin]

isn't "e" the exact value of..."e"?

The amount of digits you bother to use is what we're talking about here

 

[SHISHKABOB]

with numbers like pi and e I usually just use the calculator button >.>

and round later

 

[QuarkCharmer]

isn't "e" the exact value of..."e"?

Personally, I use \lim_{n \to +\infty}(1+\frac{1}{n})^{n} because I would hate to confuse it with 1.6*10^-19 C.

 

[drizzle]

*slaps Dashin with a big, fat, codfish*

http://files.myopera.com/Chyren/files/fishSlap1a.gif

Now you're officially one of us. Welcome to the PF cult.

That was my part Mr. Hobin!


Welcome to the forum Dashin, hope you enjoy it!

 

[Dembadon]

Welcome Dashin.

But not for e or \pi?

I round e and \pi to 3 sometimes when the mood hits me. Heck, they are both close enough to each other I might just start rounding e to \pi and \pi to e.

 

[Hobin]

That was my part Mr. Hobin!

I know. I stole it!

 

[Gokul43201]

"A Ball Falls to the Ground at accelleration of 10 Newtons per second"... It falls at 9.81 (still roughly), not 10.

Newtons per second? What a massive jerk!