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This is a bit of a wierd one,
I'm looking for a function that will convert a complex number to its real and imaginary parts, using only complex number operations.
So if you imagine I had a calculator that could do all the complex number calculations, even eqponents and natrual logs etc. But it didn't have functions to get the real part imaginary part, nor the modulus and argument.
What function should I use to get the real part of a complex number?
I hope that makes sense, (I don't actually have the crazy calculator, so don't just tell me to get a new calculator.)
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can the calculator get the conjugate of a complex value?
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nope, that'd be too easy.:(
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Format?
In thinking about this, I started to wonder about the format your proposed calculator would use for complex numbers.
If using VB, for example, I would define a complex data type consisting of two Doubles (one for real part and one for imaginary part). With this format, the real and imaginary parts of each complex number would be explicitly known.
How would any program or calculator not use some similar format? My HP calculator represents complex numbers as 2D vectors in either cartesian or polar format. It will do roots, exponentials, trig functions, et cetera with complex arguments, returning complex results. The real & imaginary parts of a complex number are explictly available when using this calculator.
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perhaps...
If such a calculator could grasp a complex number as a single entity (and do operations on it thereof) you would need a systematic way of breaking it down into it's real and imaginary parts, would you not?
But how could a calculator ever be programmed as such? :confused:
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i get the feeling that it's not possible.
I can't say for sure, but if the calculator takes the complex number as a plain entity and, say, it represents it on a plane. You can do all kinds of operations on that plane without knowing where the axis are, so it would actually be able to do all this computing. Though, i don't know how. I never used vectors in planes without axis :)
It seems to me that this calculator can do anything on that plane as long as it doesn't require to know where the axis actually are, so there's no point in asking what the components are...
i hope i'm making sense.
