x $ ^7+x^4+i(x^3+1)=0 \\ \; \\ \; \\ \therefore x^4 (x^3+1)+i(x^3+1)=0,i.e.(x^4+i)(x^3+1)=0 \\ \; \\ \; \\ \therefore (x^4+i)=0 \; and \; (x^3+1)=0 \\ \; \\ $

Consider $x^4+i=0, \;i.e. \; x^4=-i, \; i.e. \; x^4=cos\dfrac{3\pi}{2}+i sin\dfrac{3\pi}{2}$

In General, $ x^4=cos\bigg( 2n\pi + \dfrac{3\pi}{2} \bigg)+i sin \bigg( 2n\pi + \dfrac{3\pi}{2} \bigg) …