Determine the minimal polynomial $f(x)$ of the following quantities:

(a) $-6 + 2 i$ over $\mathbb{R}$, where $i = \sqrt{ -1 }$
$f(x) =$

(b) $-6 + 2 i$ over $\mathbb{C}$, where $i = \sqrt{ -1 }$
$f(x) =$

(c) $2^{ 1 / 4 }$ over $\mathbb{Q}$
$f(x) =$

(d) $\sqrt{ 13 } + \sqrt{ 5 }$ over $\mathbb{Q}$
$f(x) =$

(e) $\sqrt{ 13 } + \sqrt{ 5 }$ over $\mathbb{Q}( c )$, where $c = \sqrt{ 65 }$
$f(x) =$
(Your answer should be written using $c$, not $\sqrt{ 65 }$ )