Complex Root Calculator
MathFind all n distinct nth roots of a complex number.
All n Roots
All n distinct complex numbers that, when raised to the power n, give back the original number.
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Odeh Ahwal0people find this calculator helpful
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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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