For a positive integer n, the complex number z = r(cos(θ) + i sin(θ)) has exactly n distinct nth

Question

Amrita Bhasin · Accepted Answer

Step 1: Given the complex number z = r(cos(θ) + i sin(θ)), we want to find the nth roots of z.

For a positive integer $n$, the complex number $z = r(cos(\theta) + i sin(\theta))$ has exactly $n$ distinct $n$th roots given by $z_k = \sqrt[n]{r}(cos(\frac{\theta + 2\pi k}{n}) + i sin(\frac{\theta + 2\pi k}{n}))$