SOLUTION: x^2=-1, Find all n complex solutions of the equation of the form x^n=k

Question 951807: x^2=-1, Find all n complex solutions of the equation of the form x^n=k
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

The fundamental theorem of algebra implies that a polynomial equation of degree
has precisely solutions in the complex number system.
These solutions can be or and may be .
recall the quadratic formula and its discriminant:

using the discriminant , we are able to determine solutions which are real or complex and may be repeated
if the discriminant is than , equation has solutions

like you have here =>=>, ,
using =>=>; so, discriminant is negative and we have two complex solutions
these are =>=>or

now, find all complex solutions of the equation of the form :
=> , ,

for any there will be two solutions of the equation
and can be any number from:
()

RELATED QUESTIONS
Find all complex solutions of the equation {{{ x^4-x^3+x^2-x=0... (answered by richwmiller,CharlesG2)

Find all complex solutions of the equation:... (answered by stanbon)

1. Let X(k) denote the N-point DFT of the N-point sequence x(n) a) If x(n)... (answered by Fombitz)

find all the solutions in the complex numbers, of z^4 + z^3 + z^2 + z + 1 = 0. use:... (answered by ikleyn)

Find all the complex solutions of the equation. x^4 + i =... (answered by math_helper)

Find all solutions, real and complex, of the equation.... (answered by robertb)

For a positive integer n, the complex number zk = n r cos 𝜃 + 2𝜋k n + i sin... (answered by greenestamps)

Find all solutions of the equation x^2+x+1=0 and express them in the form... (answered by ankor@dixie-net.com)

Find all solutions, real and complex of the equation: a. x^4+x^3+x^2+x=0 b.... (answered by Alan3354)