Without finding the minimal polynomial for $\displaystyle r=i\cdot 2^{\frac{1}{3}}+i $, show the degree of said polynomial must be $\displaystyle 6 $. I know this is true because I was able to derive $\displaystyle r\text{'s} $ minimal polynomial ($\displaystyle f(x)=x^6+3x^4-9x^2+9$), but in doing so I used the assumption that it was of degree $\displaystyle 6 $ as opposed to $\displaystyle 2 $ or $\displaystyle 3 $.