a) \({(1 + i)^{2006}} = {\left( {{{(1 + i)}^2}} \right)^{1003}}\)\( = {\left( {2i} \right)^{1003}}.{i^{1003}} = - {2^{1003}}i\)
b) \({(1 - i)^{2006}} = {\left[ {{{\left( {1 - i} \right)}^2}} \right]^{1003}}\)\( = {\left( { - 2i} \right)^{1003}} = - {2^{1003}}.{i^{1003}}\) \( = - {2^{1003}}.{\left( {{i^4}} \right)^{250}}.{i^2}.i = {2^{1003}}.i\)
