Editing Mean value theorem (section)

=== Complex analysis ===
{{See also|Voorhoeve index|Mean value problem}}
As noted above, the theorem does not hold for differentiable complex-valued functions. Instead, a generalization of the theorem is stated such:<ref>1 J.-Cl. Evard, F. Jafari, A Complex Rolle’s Theorem, American Mathematical Monthly, Vol. 99, Issue 9, (Nov. 1992), pp. 858-861.</ref>

Let ''f'' : Ω → '''C''' be a [[holomorphic function]] on the open convex set Ω, and let ''a'' and ''b'' be distinct points in Ω. Then there exist points ''u'', ''v'' on the interior of the line segment from ''a'' to ''b'' such that
:<math>\operatorname{Re}(f'(u)) = \operatorname{Re}\left ( \frac{f(b)-f(a)}{b-a} \right),</math>
:<math>\operatorname{Im}(f'(v)) = \operatorname{Im}\left ( \frac{f(b)-f(a)}{b-a} \right).</math>

Where Re() is the real part and Im() is the imaginary part of a complex-valued function.