imaginary i

I own a ti-83 graphing calculactor and when I put i^7 it puts -3E-13-i and when I put i^8 it says 1-2E-13i but when I try i^10 it saysd -1. Can some explain what is going on with the calculator.

Originally posted by wormer
I own a ti-83 graphing calculactor and when I put i^7 it puts -3E-13-i and when I put i^8 it says 1-2E-13i but when I try i^10 it saysd -1. Can some explain what is going on with the calculator.

It looks to me like its aproximating. What I mean as that unlike the Ti-89, the 83 doesn't work symbolically with "i". Im not sure how "i" is defined in the 83, but its probably a series definition.

but the answers are correct with some reasoning applied to the solutions. what you calculator is saying is

i^7 is for all practical purposes -3E-13-i =0 -i = -i

Originally posted by joe shmo
It looks to me like its aproximating. What I mean as that unlike the Ti-89, the 83 doesn't work symbolically with "i". Im not sure how "i" is defined in the 83, but its probably a series definition.

but the answers are correct with some reasoning applied to the solutions. what you calculator is saying is

i^7 is for all practical purposes -3E-13-i =0 -i = -i

I understand that the accuacy deminishs on the calculator but where is this small number coming from?

Originally posted by wormer
I understand that the accuacy deminishs on the calculator but where is this small number coming from?

That comes from the fact it has only 12 digit accuracy if I remember right, I have one close to yours. I sometimes want double digit accuracy, like 24 or 36 digits but can't find a program or site that does that degree of accuracy. If it rounded out, it would go to zero but it just looks at the number the 12 digits say. I think internally it goes with 16 digits or so and it tries to put the results into a number when even at the max internal accuracy, it shows some result. What I have in front of me is the HP48G. Not sure of where to find i on it. If I do the square root of -1, it returns (0,1) just like that with the parenthesis. If I hit the square key, it gives (-1,0) presumably the real part and the imaginary part. How do you enter i? I can't even find it on the front of my 48.

Originally posted by wormer
I understand that the accuacy deminishs on the calculator but where is this small number coming from?

It probably calculates by converting to polar form and using De Moivre's formula. in polar form, i=1*(cos(pi/2)+i*sin(pi/2)). So i^7 is calculated as 1^7*(cos(7*pi/2)+i*sin(7*pi/2)). But for the calculator cos(7*pi/2) is not exactly 0, and sin(7*pi/2) is not exactly -1, becuase of rounding errors while calculating eith the real number pi.

what is 10^i

Originally posted by wormer
what is 10^i

-0.66820151019031294624233069665614235821247439584402173344902910768162624447295296623417388109718452560219201414... +
+ i*0.74398033695749318765841640687551436862460001349130482739729321475966646555830411153427150635952720096134522214...

Or the nicer 10^i = cos(log(10))+i sin(log(10))

Originally posted by Palynka
-0.66820151019031294624233069665614235821247439584402173344902910768162624447295296623417388109718452560219201414... +
+ i*0.74398033695749318765841640687551436862460001349130482739729321475966646555830411153427150635952720096134522214...

This is an answer I would give zero points to in any of my given exams.
You show how to press buttons, but not more.
I'd say FAIL.

Originally posted by FabianFnas
This is an answer I would give zero points to in any of my given exams.
You show how to press buttons, but not more.
I'd say FAIL.

And why should I care what a low life like you thinks?

http://en.wikipedia.org/wiki/Machine_precision

Originally posted by wormer
what is 10^i

In general: x^y = e^(y ln x) (x != 0)

Originally posted by David113
It probably calculates by converting to polar form and using De Moivre's formula. in polar form, i=1*(cos(pi/2)+i*sin(pi/2)). So i^7 is calculated as 1^7*(cos(7*pi/2)+i*sin(7*pi/2)). But for the calculator cos(7*pi/2) is not exactly 0, and sin(7*pi/2) is not exactly -1, becuase of rounding errors while calculating eith the real number pi.

also, (not sure if this is true for modern calculators) don't calculators often use partial sums of the taylor (or maclaurin) series to calculate cos and sin? i.e. cosx = 1 - x^2/2! + x^4/4! - ... etc.? this would create further rounding errors depending on how many terms the calculators use before deciding it's "close enough."

Originally posted by Palynka
And why should I care what a low life like you thinks?

I laugh my ass off every time I see anyone using pi with as many decimals his MathCad or Mathenmatica or calculater can produce, happily thinking that the more decimals (in this case 110 decimals 😀 ) the merrier. Giving him a zero as a result becuase he shows clearly that he doesn't know what he is doing, relying in numbers en masse.

As calling me a low life I know you're recognize the situation and giving a personal attack as a response. As my pupils do when they get that zero in his test result.

KazetNagorra gave an answer that explains almost everything, without need to give any answer to the quesiton. Salute to him!

Originally posted by FabianFnas
I laugh my ass off every time I see anyone using pi with as many decimals his MathCad or Mathenmatica or calculater can produce, happily thinking that the more decimals (in this case 110 decimals 😀 ) the merrier. Giving him a zero as a result becuase he shows clearly that he doesn't know what he is doing, relying in numbers en masse.

As calling me a l at explains almost everything, without need to give any answer to the quesiton. Salute to him!

I laugh my ass off when an idiot like you doesn't see how it was a joke relating to the opening post. Especially when David113 had already answered the question (despite your failure to salute him), it should have been pretty obvious.

But it's ok. From you I only expect idiocy.

Originally posted by Palynka
I laugh my ass off when an idiot like you doesn't see how it was a joke relating to the opening post. Especially when David113 had already answered the question (despite your failure to salute him), it should have been pretty obvious.

But it's ok. From you I only expect idiocy.

Why do you have so much anger in you? Why don't you just relax and enjoy life?