Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Complex Number Calculator

Indeed I have been working on a Complex Number Calculator

It can only do + - × / and ^ so far. And it may get those wrong.

I have had a lot of difficulty "parsing" and "walking" the formula, but I figure it is worth it - it is easier, and much more elegant, to write the formula than to enter the real and imaginary into different boxes and press function keys.

Could you pose it a few problems and see how it goes?

(Oh, and it is a real number calculator, too!)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

ryos

Member

Registered: 2005-08-04

Posts: 394

Re: Complex Number Calculator

5^i = -0.0386319699339353+0.99925350682348i
i(54i-3i^3)^5 + 9i - i^i^i + 3 = 3+601692067i
Interpreted Formula: ((((UNKNOWN(((54*i)-(3*(i^3)))))^5)+(9*i))-((i^i)^i))+3
0i + 4i - 0^0 + 0^i - i^i^i^i^i^i = -1.20787957635076+4i
i/0 = NaNNaNi
i^2i^3i^4i^5i^6i^7i^8i^9i = i
i^(2i*3i*4i*5i*6i*7i*8i*9i) = 1

I have no idea if any of these are right or wrong, but it seems to handle all sorts of weird things. (The last two seem contradictory, though.)

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El que pega primero pega dos veces.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Complex Number Calculator

i^2i^3i^4i^5i^6i^7i^8i^9i = i
i^(2i*3i*4i*5i*6i*7i*8i*9i) = 1

(The last two seem contradictory, though.)

maybe thats because the first one is (i^2)*(i^3)*(i^4) and not the second one which would be i^(2i)^(3i)

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The Beginning Of All Things To End.
The End Of All Things To Come.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Complex Number Calculator

Interpreted Formula: ((((UNKNOWN(((54*i)-(3*(i^3)))))^5)+(9*i))-((i^i)^i))+3

Well that one is obviously wrong, because it thinks i() is a function - I shall have to teach it otherwise

I hope to extend the functions it knows to sin, cos, sinh, etc etc

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Complex Number Calculator

OK I have added a heap of functions to the Complex Number Calculator.

I have done some testing, but I need more done ... please

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Complex Number Calculator

What a good idea ... I have made it respond to the Enter Key.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Complex Number Calculator

Very nice calculator. Here's something that I think might be weird, but I could have easily made a mistake.

Ryos's post made me decide to try out i^i. Its answer for that is ~0.2 + 0i.

It's a standard identity that e^(iθ) = cosθ + isinθ.
Therefore, i = e^(i*π/4)

Substituting this into the original gives [e^(i*π/4)]^i.
Using the laws of indices, we can the turn that into e^i²π/4 = e^-π/4.
But then putting that into the calculator gives you ~0.7 + 0i, even though it's equivalent to i^i.

Have I gone wrong somewhere?

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Complex Number Calculator

It's a standard identity that e^(iθ) = cosθ + isinθ.
Therefore, i = e^(i*π/4)

sin(pi/4) ≠ 1

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Complex Number Calculator

Slightly newer version (v0.91). Should be able to type in e^(-pi/4) and it figures out the right order of calculation.

I also added a "cis" format button so you can see the result in polar form. Fun with e^() type entries.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,244

Re: Complex Number Calculator

Outstanding!
The Complex Number Calculator is very good, very well created!
Initially (that was some days back), I couldn't see the number keys and the operation keys.
I used the keyboard keys, the calculator works perfectly well!
I even tried functions like  e^(i*pi) and found the results correct!
Commendable work, MathsIsFun!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.