66.(a)nn∗=(a+ib)(a+ib)∗a+ib)(a∗+i∗b∗)=(a+ib)(a−ib)=a2+iba−iab+(ib)(−ib)=a2+b2,which is always real since bothaandbare real.(b)|nm|=|(a+ib)(c+id)|=|ac+iad+ibc−i)2bd|=|(ac−bd)+i(ad+bc)|=p(ac−bd)2ad+bc)2=pa2c2+b2d2+a2d2+b2c2.But|n||m|=|a+ibc+
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.