Residue Calculator

Res(f, z₀) for contours

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Function f(z)

f(z) = 1/((z−1)(z−2))

Σ Res = 0∮ = 0 (if C encloses both)

z=1order 1

Residue−1

lim(z→1)(z−1)f = 1/(1−2) = −1

z=2order 1

Residue1

lim(z→2)(z−2)f = 1/(2−1) = 1

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About Residue Calculator

A complex residue calculator. Computes Res(f, z₀) for rational functions at their poles. Shows pole order, residue formula used, and result. Essential for contour integration via the residue theorem: ∮f dz = 2πi·ΣRes. Select from preset functions. All calculations are client-side.

Residue Calculator Features

Residue
Pole order
Residue theorem
Presets
Formula

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