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.
The set of real numbers contains the set of rational numbers as well as irrational numbers like pi, e, and the square root of two.