CVXI6

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The length of the curve L\, is \sqrt{2}.

\int_C \frac{dz}{z^4} \le \max_{z\isin C} \left|\frac{1}{z^4}\right| \cdot \mathrm{length}(C)\,

=\frac{1}{\min_{z\isin C}\left|z^4\right|} \sqrt{2} = \frac{\sqrt{2}}{\left|(\frac{1}{2}+i\frac{1}{2})^4\right|}\,

=2^{5/2}\left|\left[e^{i\frac{\pi}{4}}\right]^{-4}\right| = 2^{5/2}\left|e^{-i\pi}\right| = 2^{5/2}\,

Main Page : Complex Variables : Complex Integrals

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