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

\int _{C}{\frac  {dz}{z^{4}}}\leq \max _{{z\in C}}\left|{\frac  {1}{z^{4}}}\right|\cdot {\mathrm  {length}}(C)\,

={\frac  {1}{\min _{{z\in 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}}\,

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