Editing Function of a real variable (section)

== Complex-valued function of a real variable==

A '''complex-valued function of a real variable''' may be defined by relaxing, in the definition of the real-valued functions, the restriction of the codomain to the real numbers, and allowing [[complex number|complex]] values.

If {{math|''f''(''x'')}} is such a complex valued function, it may be decomposed as 
:{{math|''f''(''x'')}} = {{math|''g''(''x'')}} + {{math|''ih''(''x'')}},
where {{math|''g''}} and {{math|''h''}} are real-valued functions. In other words, the study of the complex valued functions reduces easily to the study of the pairs of real valued functions.