How do you find the n^{th} roots of complex numbers in polar form?

1 Answer
sankarankalyanam
Jun 14, 2018

z^(1/n) = r^(1/n) ( cos (theta/n) + i sin(theta/n))

Explanation:

Polar form of complex number is z = r( cos theta + i sin theta)

![https://www.google.com/search?q=demorvies+theorem&client=safari&hl=en-us&prmd=ivn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiYmuTisNLbAhWJwI8KHXycAGsQ_AUIESgB&biw=768&bih=922#imgrc=XMEZvta0Lgq8wM:](useruploads.socratic.org)

By De Morvies theorem,

z^(1/n) = r^(1/n) ( cos (theta/n) + i sin(theta/n))

Related questions
See all questions in De Moivre’s and the nth Root Theorems
Impact of this question
12743 views around the world
You can reuse this answer
Creative Commons License