The set of complex numbers is represented by the Latin capital letter C presented with a double-struck font face. The set of complex numbers extends the set real numbers and is visualized in the complex plane.
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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 complex numbers contains all possible complex numbers. Each complex number has a real part and an complex part.