All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.
Permanence of Algebraic Form
See also
Analytic Continuation, Continuity Principle, Elementary FunctionExplore with Wolfram|Alpha
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 380, 1985.Referenced on Wolfram|Alpha
Permanence of Algebraic FormCite this as:
Weisstein, Eric W. "Permanence of Algebraic Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PermanenceofAlgebraicForm.html