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A complex number is constructed as a pair of real numbers.  They are called the "real part" and the "imaginary part".  The term "imaginary" is unfortunate—it suggests some defectiveness in the existence of this part.  The mathematicians who had been frustrated by this problem for so long may be forgiven for using this word.

A complex number is constructed as a pair of real numbers.  They are called the "real part" and the "imaginary part".  The term "imaginary" is unfortunate—it suggests some defectiveness in the existence of this part.  The mathematicians who had been frustrated by this problem for so long may be forgiven for using this word.

Now, when one measures some ordinary quantity, like the length of a table, one gets a plain real number, and it is undertandable that one might treat the "imaginary part" of that quantity as not existing.  But, in the deeper study of mathematics, complex numbers play an enormously important role, including many real-world applications, as will be noted below.

Now, when one measures some ordinary quantity, like the length of a table, one gets a plain real number, and it is understandable that one might treat the "imaginary part" of that quantity as not existing.  But, in the deeper study of mathematics, complex numbers play an enormously important role, including many real-world applications, as will be noted below.

Complex numbers have all the normal arithmetic operations defined on them—addition, subtraction, multiplication, and division (but not by zero).  See [[Arithmetic with complex number|complex arithmetic]].

Complex numbers have all the normal arithmetic operations defined on them—addition, subtraction, multiplication, and division (but not by zero).  See [[Arithmetic with complex number|complex arithmetic]].