Complex Number Problems
Need help with my Algebra question – I’m studying for my class.
Problem 1. Find the Laurent series expansion of
f(z) = 1/ z(z + 1)
in the region 0 < |z| < 1.
Problem 2. Determine the Laurent series expansion of the function
f(z) = 1 /z(1 + z
2
)(4 − z
2
)
in the regions
a) 0 < |z| < 1, b) 1 < |z| < 2, c) |z| > 2.
Problem 3. Determine the Laurent series expansion of the function
f(z) = e^(1/z) + e^z
in the region |z| > 0.
Problem 4. Compute the residue of the function
f(z) = (1 + z^6
)^(−1) at the point z = −i.
Problem 5. Compute by contour integration
x^2/(1 + x
2
)^2
dx from 0 to ∞