Complex Root Calculator

Complex Root Calculator

Find all nth roots of a complex number using De Moivre's theorem.

Last updated: June 2026 | By Patchworkr Team

Root Finder

Enter finite real numbers. Root degree must be an integer from 1 to 10.

Input Complex Number
1
Magnitude and Angle
Magnitude: 1
Angle: 0°
Roots
Root 1
1
Root 2
-1 + 0i

What are Complex Roots?

The nth roots of a complex number are the complex numbers whose nth power equals the original value. They are evenly spaced around the origin.

How to Use It

  1. Enter the complex number.
  2. Choose the root degree.
  3. Read the list of roots on the right.

De Moivre's Formula

z = r(cos θ + i sin θ) and the nth roots are r^(1/n) with angles (θ + 2πk)/n.

What if the input is zero?

If the complex number is 0, every nth root is also 0.

Can I use decimals?

Yes. The calculator accepts finite decimals and scientific notation.

Why limit the root degree?

The new layout keeps the output readable and avoids an unbounded list of roots.

What if the degree is invalid?

Non-integers, empty input, and out-of-range values are rejected.

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