residues
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Examples forComplex Analysis

Complex Numbers »

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

Construct an analytic function:

analytic function with real part x^2 - y^2
holomorphic function imaginary part Sinh[x] Sin[y]

Determine the harmonic conjugate:

harmonic conjugate x^3 - 3 x y^2

Poles

Locate poles of a complex function:

poles of (z^2-4) / ((z-2)^4*(z^2+5z+7))
pole points of 1/(sin^2 z)
show 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
csc^7(z) residue at z=0

Compute residues at the poles of a function:

show 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:

Riemann surface log z
Riemann surface (z^3-z)^(1/3)

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