∮[(z - 1)/(z(z - t)(z - 3i)) dz] ; |z - i| = 1/2
∮f(z)/(z−a)dz=2πif(a)\oint f(z)/(z-a) dz =2\pi i f(a)∮f(z)/(z−a)dz=2πif(a)
∮[(z−1)/z(z−t)(z−3i)]dz\oint [(z-1)/z(z-t) (z-3i)] dz∮[(z−1)/z(z−t)(z−3i)]dz
∮[(z−1)/(z2−tz)(z−3i)]dz∮[(z−1)/(z^2 −tz)(z−3i)]dz∮[(z−1)/(z2−tz)(z−3i)]dz
=∮[((z−1)/(z2−tz))/z−3i]dz=2πf(a)=\oint [( (z-1)/(z^2-tz))/z-3i] dz = 2\pi f(a)=∮[((z−1)/(z2−tz))/z−3i]dz=2πf(a)=2πi[((t−1)ln(∣z−t∣))/(t2−3it)+((1−3i)ln(∣z−3i∣))/(3it+9)+((i)ln(∣z∣))/3t]=2\pi i[ ((t-1)ln(|z-t|)) /(t^2-3it)+((1-3i)ln(|z-3i |)) /(3it+9) +((i) ln(|z|))/3t]=2πi[((t−1)ln(∣z−t∣))/(t2−3it)+((1−3i)ln(∣z−3i∣))/(3it+9)+((i)ln(∣z∣))/3t]
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