(adsbygoogle = window.adsbygoogle || []).push({}); Find [tex] \int_{C} 3(z-i)^2 dz [/tex] where C is the circle |z-i|=4 traversed once clockwise

well i know it is zero but i just want to prove it.. kind of

so we can parametrize [tex] z(t) = i + 4e^{it}, \ 0\leq t \leq 2 \pi [/tex]

so

[tex] \int_{C} 3(z-i)^2 dz = \int_{0}^{2\pi} 3(i + 4e^{it}-i)^2 (4ie^{it}) dt [/tex]

is the setup good?

Also

Compute [itex] \int_{\Gamma} \overline{z} dz [/tex] where Gamma is the circle |z|=2 tranversed once counterclockwise

[tex] z(t) = 2e^{it} [/tex]

[tex] \int_{0}^{2\pi} (-2e^{it}) (2i e^{it}) dt [/tex]

is this correct??

Thank you for the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Contour Integrals

**Physics Forums | Science Articles, Homework Help, Discussion**