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)
plot a complex function
plot z^4
Poles
locate poles of a complex function
poles of (z^2-4) / ((z-2)^4*(z^2+5z+7))
poles of 1/(sin^2 z)
poles of Gamma(z)
locate poles in a specified domain
poles of z tan(iz) with 0 < Im z < 12
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)
compute residues at poles in a specified domain
residues of 1/(e^(2z)+1) with |z| < 3pi
Riemann Surfaces
visualize a Riemann surface