(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

evaluate

[tex] \int_{c} | z - 1 | |dz| [/tex]

where c is the positive oriented unit circle.

2. Relevant equations

3. The attempt at a solution

[tex] | z - 1 | = \left[ ( z-1)( \overline{z} - 1 ) \right] ^{1/2} = \left[ |z|^{2} - z - \overline{z} +1 \right] ^{1/2} [/tex]

[tex] c : z(t) = e^{it} ; 0 \leqslant t \leqslant 2\pi [/tex]

[tex] |dz| = dt[/tex]

[tex] |z| = 1 [/tex]

[tex] \int_{c} | z - 1 | |dz| = \int_{0} ^{2 \pi} (2 - e^{it} - e^{-it}) ^{1/2} dt[/tex]

[tex] \int_{0} ^{2 \pi} \sqrt{2-2 \cos t } dt [/tex]

Is this right so far? What to do next? :S

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# Homework Help: Complex integration problem

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