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Definition of COMPLEX NUMBER
: a number of the form a + b√‒̅1̅ where a and b are real numbers
First Known Use of COMPLEX NUMBER
Any number consisting of both real numbers and imaginary numbers. It has the form a + bi, where a and b are real numbers and i = ; a is called the real part and bi 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 equations such as x2 + 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 (seefield theory).