z^n = K (K is real).The sum of the arguments of all the roots of this equation is an odd multiple of pi..When is this possible? That is the relation between n and k.

Dear Aniket,

The sum of all the roots of zⁿ=K is an odd multiple of π when K is negative.

Roots of this equation for K<0 will be z=|K|^1/ne^i(2m+1)π/n where m=0,1,2,...,n-1. Clearly the sum of roots is an odd multiple of π.

e.g. z³=-1

=> z=e^iπ/3,e^iπ,e^i5π/3

Sum of arguments = 3π

Hope this helps.

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