I don't think, there is a way. Not without destroying information.

But it is surprising that you get complex numbers as a result of experimental measurements.

If you were to restrict the set of complex numbers, the answer is, it's possible.  In general, I don't think so (I'd imagine you are using a computer anyways, doubt you'd need full fledged real numbers in the data) without losing some information.  Here's one way you can if you are working with floating point numbers to represent the complex number (so we are restricting the set of complex numbers).

 A complex number with given precision (in bits) can be encoded as two floating point numbers (reals with a fixed precision), a pair (r,i), one with K bits and the other with L bits.  Encode it as a string as follows:

1)   Encode the the bits of r (K bits).

2)  Encode the bits of i (L bits).

To decode (given two numbers, K, and L):

1) Read the first K bits, store these bits as a floating point number (the "real" part)

2) Read the next L bits, store these bits as a floating point number (the "imaginary" part).

These scheme requires K + L bits, and knowing K and L beforehand (K and L may be the same or some fixed value for the data type).  The restriction comes from precision and the size the numbers may be.  Works well, and simple enough to be pragmatic for any K and L you give in the scheme.  You can always add a separating symbol too if you don't want to give K and L, but this does increase the storage cost of the data.  This works well for non-negative values, so you can of course build more on this scheme.  The sequence of bits can represent a number, but it is better to keep it as a string as most data types don't give you the flexibility you may want.

Hope this helps!

If you have any additional details to help researchers answer this question, provide more details.  I don't know much more about the data you are using.  

Thank you everyone for the input.

I really can't separate the real and imaginary part of the complex number into two different attributes, since there are several layers of pattern recognition process, including feature selection and classification. If the numbers are separated, the real part may be selected while the imaginary is not, or vice versa.

As for Daniel Page's answer, while the process will indeed produce a unique number, this number doesn't actually reflect the original numbers, as the resulting number is fluctuating (sometimes it's very high when both parts are very low, etc), and hence deteriorate the classification results. But again, thanks anyway.

I decided to transform the complex number to the polar coordinates, and came across to pairing function concept, which is capable to map two non-negative integers into single integer, and the number itself is unique and consistent. I found Cantor's and Szudzik's pairing function to be very interesting and useful, however it is explicitly stated that these two functions are to be used for natural numbers. Therefore, is there any other pairing functions that is suitable for real numbers?

In order to find the most appropriate pairing function, you should first determine the set of values you can obtain, average, standard deviation for r and teta and the boundaries.

For instance, let's assume that the maximum value for r is 10 with 4 digits accuracy and teta fluctuates between 0 and 2pi with 4 digits accuracy.

Then the idea is to separate two consecutive values of r (5.001 and 5.002 for instance) by 10000 possible values for teta.

For example, first you keep only 4 digits for r    ( e.g., r = round(r*1000)/1000    )

and then you can try f(r,teta) = r + teta/10000

However, if the precision of your numbers is too high (e.g., 10 digits accuracy), this approach might not be appropriate.

Dear Fajri Pratama

You look before the world mathematical community as the module on the complex plane with impotentny argument (forgive me for sad humour). Dear Fajri Pratama find to yourself the mistress or present to your girl or to the wife a box of chocolate truffles. Only then before you the world of natural and imaginary numbers, the main thing, in this question strong argument will open in all beauty.

Alexander

I am wondering if your data is a set of 120 segments of sampled signal containing the result of a wavelet computation with complex wavelets. In this case (and also some similar cases) it would be more practical to consider instead of complex values, just their absolute values, which are positive reals, and make a statistical analysis on the resulting data set. Also, a separated data set can contain the phases \phi of the complex numbers. Make a statistical analysis with this set also. Finally you can unify the conclusions and make your Interpretation.

If the real and imaginary parts are natural numbers, then you can construct a one-to-one mapping of natural numbers to pairs of natural numbers. Take a look at the countability of rational numbers.

http://www.oxfordmathcenter.com/images/notes/174-00.png

Converting complex number into real number is not possible directly, but by finding magnitude(Modulus) we are able to order the complex numbers

Normalized these converting complex numbers, using the sin function to express.

Check Cantor pairing function in wikipedia which encodes two natural numbers into a single natural number. however, fractions and negative numbers still unkown for me until now?