Demoivre's Theorem Program Problems
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  • Demoivre's Theorem Program Problems
  • 06 May 2014 05:13:32 pm
  • Last edited by MrDew25 on 06 May 2014 05:27:10 pm; edited 1 time in total
If you don't know, Demoivre's Theorem is a way to find out the powers of complex number, such as (1+i)^5.

Right now, I am having trouble with a variable not stopping. Here is the code for my program. By the way, I will be editing the code to match the corrections when they become available.
Code:
ClrHome
1->P
1->Q
1->R
1->S
Disp "(a+bi)^n"
Input "a: ",A
Input "b: ",B
Input "n: ",N
If abs(A/S)=1 and abs(B/S)=1
Goto C
Lbl S
If A/S<=1 and A/S>=~1
Then
If B/S<=1 and B/S>=~1
Then
Goto B
Else
Goto C
End
Else
Goto C
End
End
Lbl C
If Q=1
Then
~Q->Q
sqrt(2)P->P
P->S
Goto S
End
If Q=~1
Then
~Q->Q
2+R->R
R->S
Goto S
End
Lbl B
cos^-1(A/S)->C
sin^-1(B/S)->D
C/5->G
D/5->H
If iPart(G)!=G and iPart(H)!=H
Goto C
If A<0 and B>0
180-D->D
If A<0 and B<0
Then
360-C->C
180-D->D
End
If A>0 and B<0
~C->C
cos(NC)->E
sin(ND)->F
If fPart(F)=~2|E~13 or fPart(F)=~4|E~13
iPart(F)->F
(S^N)(E+Fi)->E
ClrHome
Output(1,1," The Answer Is: ")
Output(2,1,E)
Pause
ClrHome
Output(1,1,"")
First problem: This line doesn't do what you think it does.
Code:
If A/S=1 or ~1 and B/S=1 or ~1
Check out my correction to see the steps of fixing it:
Code:
If A/S=1 or A/S=~1 and B/S=1 or B/S=~1  // sort of correct
If (A/S=1 or A/S=~1) and (B/S=1 or B/S=~1) // definitely correct
If abs(A/S)=1 and abs(B/S)=1 // even better
I will try that then, but what did it do?


Well, in TI-BASIC, you cannot chain commands like most other programming languages.

If A=1 or -1

means

If A=1 or If -1; Which will always be true. You have to specify each variable as you check it.
MrDew25 wrote:
I will try that then, but what did it do?
In conditional expressions (see chapter 3 of my awesome and shamelessly-plugged book), any zero value is equivalent to false and any non-zero is equivalent to true. The calculator reads that line as: If <something> or true and <something> or true, because -1 is nonzero and therefore true. Thus, that line is always true and always runs the following Goto command. The " or " command is not for specifying options to the = sign, but for specifying sets of conditions, any one of which can be true to make the whole expression true.
I think that the problem lies somewhere inside Label C. Correct me if I am wrong.


Separate from any other issue, I notice you Goto from inside a Then/End block, which is a memory leak and to be avoided. You should restructure your code so that any conditional Gotos are just If/Goto, never If/Then/Goto/End. Anyway, it would probably help if you told us a little bit about what the algorithm is supposed to be and what the code at Lbl B, C, and so on is supposed to do.
Would a If/Then/Goto/Else/Goto work?
Lbl C is the main label. As the theorem takes complex number raised to a power, (1+i)^5, and changes them into their trigonometrical form, which is r^n(cosnθ + isinnθ) (r is the radius, n is the power and θ is the angle). In our case, it is sqrt(2)^5(cos5θ + isin5θ) Lbl C finds the radius. Lbl B finds the angle and then puts everything together.
Ok, I edited the issue that you talked about Kerm to this
Code:
Lbl S
If A/S<=1 and A/S>=~1
Goto D
Lbl D
If B/S<=1 and B/S>=~1
Goto B
If A/S>1 or A/S<~1
Goto C
If B/S>1 or B/S<~1
Goto C
Okay, here's my attempt: (Not sure if this is right or not, but here it goes:)


Code:
ClrHome
Disp "(A+B[i])^N
Prompt A,B,N
Fix 3
tan^-1(B/A
(sqrt(A^^2+B^^2)^N)(cos(Ans)+[i]sin(Ans


Does this work right for you? (Probably doesn't; I need some example problems to check it really quick...)

EDIT: Nope, doesn't work... Let's see where I went wrong...

EDIT: WHY?
The code worked. The code I used was
Code:
ClrHome
Disp "(A+B[i])^N
Input "A: ",A
Input "B: ",B
Input "N: ",N
tan^-1(B/A)->C
(sqrt(A^^2+B^^2)^N)(cos(NC)+[i]sin(NC)
which came from you. Great job
MrDew25 wrote:
Would a If/Then/Goto/Else/Goto work?
No, that's still a Goto inside a Then/End, and has the same memory leak problems. Also, please do not double-post, and definitely do not triple-post. I recommend you read A Brief Introduction to Better Netiquette.
Sorry, I haven't been a forum in a while.

EDIT: And ok, I understand. See, I am a fast learner.
MrDew25 wrote:
The code worked. The code I used was
Code:
ClrHome
Disp "(A+B[i])^N
Input "A: ",A
Input "B: ",B
Input "N: ",N
tan^-1(B/A)->C
(sqrt(A^^2+B^^2)^N)(cos(NC)+[i]sin(NC)
which came from you. Great job


Oh wow, thanks! Knew I was forgetting something important... Those pesky N's!

Also, here's a really optimized piece:


Code:
ClrHome
Disp "(A+B[i])^N
Prompt A,B,N
Ntan^-1(B/A
(sqrt(A^^2+B^^2)^N)(cos(Ans)+[i]sin(Ans
  
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