I have simplified this cube root:
$$ \sqrt[3]{1+i}=\sqrt[6]{2}\bigl(\frac{\sqrt{6} + \sqrt{2}}{4} +{\frac{\sqrt{6} - \sqrt{2}}{4} }i\bigr)$$ which is simplified algebraic expression form.
Now, I was wondering if you can simplify this cube root in different simplified form ?
Like this : $$ \sqrt[3]{1+i \sqrt{3}} =A + Bi \space\space\space\space\space?$$
Where $A$ and $B$ are constant numbers.
Or any simplified algebraic expression form? Other than non-algebraic form like these: $$ \cos(\theta) +i \sin(\theta) $$ or $$ e^{i \theta} $$