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There is rule for a number to belong to the set of real numbers. It's called 'Law of Tricotomy'. According to it, "Any two numbers a, b are real if and only if one of the following holds true (i)ab. In short a number is real if and only if it can be compared (like lesser than or greater than or is equal to). As for the question 0 can be compared, right? Hence, 0 is a real number.
0 0 0
0 can be expressed as 0=0+0i. In that sense, 0 is a complex number. 
This question can also be answered in another way.
Every real number can be expressed in the form a+ib. For example 1=1+0i. Thus every real number is a complex number.
0 0 0
not satisfied
It is true that every real number is a complex number. But imaginary (purely) are the ones in which real part is 0 and imaginary part is non zero real number.
Dear friend set of real numbers (R) is a subset of the set of all complex numbers (C). That is R is contained in C. Thus by set properties every element in R belongs to C. 0 being a real number thus belongs to C.
Complex numbers and (purely) imaginary have a little difference. Complex numbers are divided into two sets one being set of real numbers and the other being set of imaginary numbers. 0 doesn't belong to imaginary number set.
And I am not your friend
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