If z is a complex number satisfying ${\mathrm{z}}^4 + {\mathrm{z}}^3 + 2{\mathrm{z}}^2 +\mathrm{z} + 1 = 0$ then $\left|z\right|$is equal to

$$\begin{gathered} {\mathrm{z}}^4+{\mathrm{z}}^3+2{\mathrm{z}}^2-\mathrm{z}+1=0 \\ \Rightarrow ({\mathrm{z}}^4+{\mathrm{z}}^3+{\mathrm{z}}^2)+({\mathrm{z}}^2+\mathrm{z}+1)=0 \\ \Rightarrow {\mathrm{z}}^2({\mathrm{z}}^2+\mathrm{z}+1)+({\mathrm{z}}^2+\mathrm{z}+1)=0 \\ \Rightarrow ({\mathrm{z}}^2+\mathrm{z}+1) ({\mathrm{z}}^2+1)=0 \\ \therefore {\mathrm{z}}^2+\mathrm{z}+1=0 \mathrm{or} {\mathrm{z}}^2+1=0 \\ \Rightarrow {\mathrm{z}}^2=-1={\mathrm{i}}^2 \\ \Rightarrow \mathrm{z}=\mathrm{w} \mathrm{or} {\mathrm{w}}^2 \mathrm{or} \mathrm{z}=\pm {\mathrm{i}}^2 \\ \boxed{\therefore \left|\mathrm{z}\right| =1} \end{gathered}$$