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Wolfram|Alpha: simultaneous equations w/ imaginary numbers?

GROUPS:

I'm trying to solve a simultaneous equation that involves imaginary numbers. The first problem I'm finding is that Wolfram|Alpha wildly misinterprets anything that to me makes sense and every imaginary number needs brackets around it so that it is not misinterpreted.

I have put in the following after some corrections to try and get wolfram to properly interpret what I want:

((120-a)/2)+(a/(-i5))+((b-a)/(-i5))+((14.14+i14.14)/-i5)=0, ((b-i120)/4)+(b/(i4))+((a-b)/(-i5))+(-14.14-i14.14)/(i4))=0

However it completely misunderstands this and is not interpret it as two equations. I get something that to me is ggodibigook and it makes a rough attempt at solving for B. It's quite possible the equations are totally wrong but the fact that the website completely misinterprets what I am putting in because maybe it is trying to be too clever means that I am totally none the wiser.

I tried to misuse this or am I formatting my input incorrectly?

POSTED BY: Simon Turner
Answer
9 months ago

For equations you should use == , and the imaginary unit is I

eq1 = ((120 - a)/ 2) + (a/(-I 5)) + ((b - a)/(-I 5)) + ((14.14 + I 14.14)/-I 5) == 0

eq2 = ((b - I 120)/4) + (b/(I 4)) + ((a - b)/(-I 5)) + (-14.14 - I 14.14)/(I 4) == 0

Solve[{eq1, eq2}, {a, b}]


{{a -> -55.1829 + 126.834 I, b -> -36.4162 + 84.4572 I}}
POSTED BY: Hans Dolhaine
Answer
9 months ago

Ok, well I'm quite confused here because if i use "i" it says that it is taking "i" as the imaginary unit, the example of simultaneous equations simply states the two equations using "=" not "==" (as used in C) with no extra "code" to tell it what to do. Is there a reference to the Wolfram code/language ? this all seems far more complex than needs be.

POSTED BY: Simon Turner
Answer
9 months ago

I have also found that altering the equation gets a difference result in how it is interpreted

POSTED BY: Simon Turner
Answer
9 months ago

Well, what do you mean by "altering the equation"? And what do you mean by "wolfram"?

I am using Mathematica (Version 7 , Windows 7) and I have essentially no idea of Wolfram Alpha, I suggest you buy a Mathematica - this had the advantage that you can post notebooks to show what you mean - smile.

POSTED BY: Hans Dolhaine
Answer
9 months ago

Err wolfram as in the main website. I have already shelled out money to join wolfram, now i need to spend more money for matematica ? this is starting to sound like a racket. Apparently distance learning students don't exist, if I want to buy a student lisence I have to post a link to a page on my university website that shows me as a student........

POSTED BY: Simon Turner
Answer
9 months ago

Hmmm. I find your wording somewhat indecent and agressive.

If you gave money already - ok, that is so. Anyhow I can only recommend to buy a Mathematica. You have a really profound documentation, you can do incredible lots of calculations and document them, you can write reports (it has a sort of integrated text-system), you can prepare slide-shows (not bad if you are a student and have to show something in a seminar), you can make charts and no - I am not an employee of Wolfram, but I have my experiences with Mathematica.

Wolfram Alpha may be great - but as I mentioned I do not know it. But Mathematica is simply great.

So - go on. If you have uncles and aunties have them make it a gift for you - smile.

POSTED BY: Hans Dolhaine
Answer
9 months ago

my problem here is the total confucion the website brings, there is no clear explanation as to what does what and while I can afford it I don't see why I should be paying for something that I think I already paid for. Either this site works or it does not. I am no mathematician and i don't buy this story that if I simply buy this program or whatever it is I will suddenly understand math and pass my grades. All I want is to solve simultaneous equations with complex numbers.

POSTED BY: Simon Turner
Answer
9 months ago

WolframAlpha appears to correctly interpret this

Solve with two equations

Perhaps you can compare that with what you used, see if you can track down any differences and see if those differences matter. You might be missing a pair of ( ) in your original posting because in most cases you have /(-I 5) or /(I 4) but in one place you have /-I 5 and that worries me. If you have more than one item in a denominator then those need to be wrapped inside ( ). I did eliminate some ( ) in my WolframAlpha input which appeared to not be essential.

WolframAlpha doesn't support assigning expressions to variables and then using those variables in expressions. And it has a limit on line length so you sometimes have to get creative in finding a way to make expressions short enough. Sometimes you can try to get around this by solving part of your problem using Wolfram alpha and then substitute that solution into a second query to get your final answer.

POSTED BY: Bill Simpson
Answer
9 months ago
In[14]:= eq1 = ((120 - a)/2) + (a/(-I 5)) + ((b - a)/(-I 5)) + 
    5 ((14.14 + I 14.14)/-I ) == 0 // FullSimplify

Out[14]= (-10.7 + 70.7 I) + (0. + 0.2 I) b == 0.5 a

In[15]:= eq2 = ((b - I 120)/
      4) + (b/(I 4)) + ((a - b)/(-I 5)) + (-14.14 - I 14.14)/(I 4) == 0 // FullSimplify

Well, it seems that I get your results:

Out[15]= (-132.325 + 17.675 I) + (1. + 0. I) a - (2.25 + 1.25 I) b == 0

In[16]:= Solve[{eq1, eq2}, {a, b}] // Rationalize

Out[16]= {{a -> -(319233/5785) + (733732 I)/5785,  b -> -(84267/2314) + (97717 I)/1157}}
POSTED BY: Hans Dolhaine
Answer
9 months ago

Yes moving brackets around seems to make it work. what is the character limit? is there an easier way of entering this stuff ?

I mean for something that promises to be this sofisticated it would be nice to have a text box to enter stuff into rather than a single line.

POSTED BY: Simon Turner
Answer
9 months ago

I'm glad you seemed to get your calculation to work.

I think I recall that the free version has a limit of about 128 characters. I believe that paying for the Pro version removes that limit and provides some other features. I have never found those clearly enough explained to get me to try that.

For anything other than really simple examples I prepare my text using other programs and then paste the text into the box.

POSTED BY: Bill Simpson
Answer
9 months ago

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