How to find the cube roots of 8+0i. Roots of Complex Numbers

[lawrencejelsma]

You made a great video for finding nth roots of r cis(∆) with clear illustrations. The reason why k = 0, 1, 2, ... n-1 is that with the nth root mathematics the nth root operator took a domain out from 0 to (2πn or 1080 degrees) into the range from 0 to 2π (or 360 degrees). For your example the last root k=2 came from a point that lied in the 720 degree to 1080 degree complex polar plane. The middle root expanded domain had a point that lied in the 360 to 720 degree complex plane. The initial root was in the 0 to 360 degree plane of cube root 8 cis(0).