Any number consisting of both real number s and imaginary number s.
It has the form a + b i , where a and b are real numbers and i = -1; a is called the real part and b i the imaginary part. Because a or b can equal 0, any real or imaginary number is also a complex number. Invented as an extension of the real numbers so that certain algebraic equation s such as x 2 + 1 = 0 would have solutions, the complex numbers form an algebraic field, meaning that they obey the commutative law and the associative law (with respect to addition and multiplication), as well as certain other rules in much the same way real numbers do (see field theory ).