It is a desirable question of the students : can we find squre root cube root …nth root of any complex number, Yes we can find it in different ways . To understand it consider a unit circle .The n th roots of unity must lie on a unit circle.
Another useful application is demoivre’s theorem.To use this first of all we will right the given complex number in polar form and then demoivre’s theorem can be used to find different roots of the given complex numbers.Remember always take the principle value of argument of complex number and write it in generalised form by adding 2nΠ in the magnitude of argument .
To read more click on the following link :
Ganit Mantra Series :Complex Numbers-04
Don’t forget to read previous discussions with the links:
Ganit Mantra Series : Complex Number -03
Ganit Mantra Series : Complex Number -02
Ganit Mantra Series : Complex Number-1
