Complex Analysis
do basic arithmetic on complex numbers
((3+4i)/5)^10
apply functions to complex numbers
exp(24+2i)
Complex Functions
compute properties of a function of a complex variable (use the variable z)
e^z
sqrt(z)
Residues
compute the residue of a function at a point
residue of 1/(z^2+4)^2 at z=2i
residue csc^7(z) at z=0
compute residues at the poles of a function
residues (z^2-9)/(z^3-3z^2+2z)
Riemann Surfaces
visualize a Riemann surface
Riemann surface log z
Riemann surface (z^3-z)^(1/3)