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CSS Pure Mathematics QUESTION #4127
Question 1
Using Cauchy Residue Theorem, evaluate $\oint_{|z|=2} \frac{5z - 2}{z(z-1)} \, dz$. The poles inside are at:
  • $z = 0$ only
  • $z = 1$ only
  • $z = 0$ and $z = 1$✔️
  • No poles inside $|z| = 2$
Correct Answer Explanation
Poles at $z = 0$ and $z = 1$. Both satisfy $|z| < 2$, so both are inside the contour.