Question

What are the complex roots of X^3 + X^2 + X + 1

Express them both in standard form and in exponential notation

Answer 1

\[x ^{3}+x ^{2}+x+1=(x+1)(x ^{2}+1)\]

Answer 2

So the real root is -1 and the complex roots are positive or negative i or positive or negative (-1)^1/2

Answer 3

\[x ^{2}=-1, x=\pm(i), or,\pm \sqrt{-1}\]

Answer 4

\[\pm \sqrt{-1}= \pm(-1)^{-\frac{1}{2}}\]

Answer 5

thanks!