How this calculation works
For nonzero z the roots lie on a circle at equal angular spacing of 360°/n.
THE FORMULA
Root magnitude = |z|^(1/n), θₖ = (arg z + 2πk)/nA worked example
The fourth roots of −1 lie at 45°, 135°, 225°, and 315°.
Good to know
Zero has a single distinct root.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
List every complex nth root in rectangular coordinates.
The primary result is labeled “Distinct roots”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Zero has a single distinct root.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The fourth roots of −1 lie at 45°, 135°, 225°, and 315°.
Which rule does this calculator apply?
Root magnitude = |z|^(1/n), θₖ = (arg z + 2πk)/n