A number ω is called an nth root of a complex number z, if ωn = z.
Working rule to find the nth roots of a complex number:
Step 1: Write the given number in polar form.
Step 2: Add 2kπ to the argument.
Step 3: Apply De Moivre’s theorem and bring the power to inside.
Step 4: Put k = 0, 1 … up to n−1.
The nth roots of unity are 1, ω, ω2 … ωn−1.
ωn = 1
Sum of the roots is 0.
1 + ω + ω2 + … + ωn–1 = 0
The roots are in G.P with common ratio ω.
Product of the roots = (−1)n+1