The set of complex numbers extends the Set of Real Number and is defined in the form of , where represents the square root of negative one and and are members of the set of real numbers. The set is denoted using the latin capital letter presented in a double-struck type face as the symbol .

A complex number is an extension of the real number line where in addition to the "real" part of the number there is a complex part of the number. The properties of complex numbers are useful in applied physics as they elegantly describe rotation.