17/06/07 01:55:11.79 tdtuxMXa.net
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complexexpand[ re[(x+I y) (-1)^(-1/6)]^2/4+im[(x+I y) (-1)^(-1/6)]^2]
expand[ {x,y}.{{7,-3 sqrt[3]},{-3 sqrt[3],13}}.{x,y}/16]
eigensystem[ {{7,-3 sqrt[3]},{-3 sqrt[3],13}}/16]
expand[ {{cos[Pi/6],sin[Pi/6]},{-sin[Pi/6],cos[Pi/6]}}. {{7,-3 sqrt[3]},{-3 sqrt[3],13}} .{{cos[Pi/6],-sin[Pi/6]},{sin[Pi/6],cos[Pi/6]}}/16]
expand[{x,y}.{{cos[Pi/6],-sin[Pi/6]},{sin[Pi/6],cos[Pi/6]}}. {{1/4,0},{0,1}}.{{cos[Pi/6],sin[Pi/6]},{-sin[Pi/6],cos[Pi/6]}}.{x,y}]