[tex]( \frac{1-i}{ \sqrt{2} } ) ^{24} = \frac{(1-i) ^{24} }{ (\sqrt{2} ) ^{24} } = \frac{[(1-i) ^{2}] ^{12} }{2 ^{ \frac{1}{2}*24 }} = \frac{(1-2i+ i^{2}) ^{12} }{2 ^{12} } = \frac{(1-2i-1) ^{12} }{2 ^{12} } = \frac{(-2i) ^{12} }{2 ^{12}} = [/tex][tex]\frac{2 ^{12} *i ^{12} }{2 ^{12}} = i^{12} =( i^{2} ) ^{6} =(-1) ^{6} =1[/tex]
