Work out roots of complex number instantly with clear inputs, formula shown and shareable results.
A non-zero complex number has exactly n distinct nth roots, all of modulus r^(1/n) and with arguments (θ + 360k)/n. They sit at the vertices of a regular n-gon centred on the origin.
nth roots
zₖ = r^(1/n)·[cos((θ + 360k)/n) + i·sin((θ + 360k)/n)], k = 0 to n − 1
All have modulus 2, with arguments 30°, 120°, 210° and 300° — spaced 90° apart.
Because adding 360° to the argument gives the same number but a different root after dividing by n, cycling through n distinct values.