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

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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))#

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