Using the parametric representation z(t) = e^(it)= cost + isint how do we evaluate the following integral (a) integral from 1 to -1 (1/z)dz along |z|=1, the upper half plane.
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Originally Posted by sandy Using the parametric representation z(t) = e^(it)= cost + isint how do we evaluate the following integral (a) integral from 1 to -1 (1/z)dz along |z|=1, the upper half plane. I'm not quite sure what you're asking. Is it to evaluated with ?
If , then [tex]\frac{1}{z}= z^{-1}= e^{-i\theta}, of course. As goes from 0 to [itex]\pi[/itex], z with go over the upper unit semicircle so z covers C. Since it is also true that you can do that integral in terms of sin and cosine.
Originally Posted by Drexel28 I'm not quite sure what you're asking. Is it to evaluated with ? Yes thats reight im asking that and the integral is from -1 to 1
Originally Posted by HallsofIvy If , then [tex]\frac{1}{z}= z^{-1}= e^{-i\theta}, of course. As goes from 0 to [itex]\pi[/itex], z with go over the upper unit semicircle so z covers C. Since it is also true that you can do that integral in terms of sin and cosine. is the answer -2i ??
Originally Posted by sandy is the answer -2i ?? can someone please check if this is right
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