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189-249B: Honors Complex Variables
Assignment 2
Due: Friday, January 30.
1. Stein, page 25, exercise 5.
2. Let $a$ and $b$ be distinct complex numbers.
Write down the power series expansion of
the function $f(z) = \frac{1}{z-a}$ around $b$. What is its radius
of convergence?
3. Stein, page 28, exercise 13.
4. Stein, Page 28, exercise 14.
5. Stein, Page 28, exercise 15.
6. Stein, Page 28, exercise 16 (a), (b) and (c).
7. Stein, Page 29, Exercise 19.
8. For an integer $m\ge 1$, write down the power series expansion of $\frac{1}{(1-z)^m}$ about
$z=0$. What is the radius of convergence of this power series?
9. Stein, Page 30, Exercise 25.
10. Stein, Page 31, Exercise 26.