If C is a closed contour in the complex plane parametrized by z(t)=u(t)+i*v(t), can there be any point where z'(t)=0?
2026-04-04 09:22:55.1775294575
can the derivative of a closed complex contour at any point be zero?
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Yes, as was shown by Daniel Fischer: $$z(t) = e^{it^3}; \quad t\in [-\sqrt[3]{\pi},\sqrt[3]{\pi}]$$
(Or take any closed contour and compose its parametrization with $(t-a)^3$.)