a) \(\dfrac{1}{{\sqrt 2 - i\sqrt 3 }} = \dfrac{{\sqrt 2 + i\sqrt 3 }}{5}\)\( = \dfrac{{\sqrt 2 }}{5} + \dfrac{{\sqrt 3 }}{5}i\)
b) \(\dfrac{1}{i} = \dfrac{i}{{{i^2}}} = - i\)
c) \(\dfrac{{3 - 2i}}{{1 + i\sqrt 5 }} = \dfrac{{(3 - 2i)(1 - i\sqrt 5 )}}{6}\)\( = \dfrac{{3 - 2\sqrt 5 }}{6} - \dfrac{{3\sqrt 5 + 2}}{6}i\)
d) \(\dfrac{1}{{{{\left( {3 + i\sqrt 2 } \right)}^2}}} = \dfrac{{{{\left( {3 - i\sqrt 2 } \right)}^2}}}{{{{\left( {3 + i\sqrt 2 } \right)}^2}{{\left( {3 - i\sqrt 2 } \right)}^2}}}\)\( = \dfrac{{{{\left( {3 - i\sqrt 2 } \right)}^2}}}{{{{\left[ {\left( {3 + i\sqrt 2 } \right)\left( {3 - i\sqrt 2 } \right)} \right]}^2}}}\) \( = \dfrac{{{{\left( {3 - i\sqrt 2 } \right)}^2}}}{{{{11}^2}}}\) \( = \dfrac{7}{{121}} - \dfrac{{6\sqrt 2 }}{{121}}i\)
