6. Let the path ( gamma ) consist of the straight line segment from 1 to ( 1+3i ), followed by the straight line segment from ( 1+3i ) to ( -3+3i ) and followed by the straight line segment from ( -3+3i ) to -3. Show that [ left| int_{gamma} frac{e^{z} sin z}{z^{2}} dz ight| leq 10e cosh 3 ]
Added by Aaron A.
Step 1
- The second segment from \( 1+3i \) to \( -3+3i \) can be parameterized as \( z(t) = 1 + 3i - 4it \) for \( 0 \leq t \leq 1 \). - The third segment from \( -3+3i \) to -3 can be parameterized as \( z(t) = -3 + 3it \) for \( 0 \leq t \leq 1 \). Show more…
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