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Complex Root Calculator

Math

Find all n distinct nth roots of a complex number.

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-1,000,0001,000,000
-1,000,0001,000,000

All n Roots

1.0000+0.0000i, -0.5000+0.8660i, -0.5000-0.8660i

All n distinct complex numbers that, when raised to the power n, give back the original number.

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Odeh Ahwal

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Odeh Ahwal
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Frequently Asked Questions

How many nth roots does a complex number have?

Exactly n distinct roots, all with the same magnitude but evenly spaced in angle around a circle, 360/n degrees apart from each other.

How are the roots calculated?

Each root has magnitude equal to the nth root of the original number's magnitude, and angle equal to (original phase + 360*k) / n degrees, for k = 0, 1, ..., n-1.

What is a real-world example of this?

The cube roots of 1 (finding all w where w^3 = 1) are 1, and two complex numbers -0.5 +- 0.866i, evenly spaced 120 degrees apart around the unit circle.

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