To find the root of the complex number a+ib, you find the arcotangent below 90 degrees of the complex ratio a/b, and then divide it by the root required. The cotangent of the result gives one of the say 3 roots of the complex ratio. For the other two roots you add on to the arcotangent 360 degrees and then 720 degrees. This procedure applies for all integer roots of complex numbers, so that there are always n nth roots of a complex number.

## Roots of Complex Numbers

To find the root of the complex number a+ib, you find the arcotangent below 90 degrees of the complex ratio a/b, and then divide it by the root required. The cotangent of the result gives one of the say 3 roots of the complex ratio. For the other two roots you add on to the arcotangent 360 degrees and then 720 degrees. This procedure applies for all integer roots of complex numbers, so that there are always n nth roots of a complex number.