p39_066 - 66. (a) nn = = (a + ib)(a + ib) = (a + ib)(a + i...

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66. (a) nn =( a + ib )( a + ib ) a + ib )( a + i b )=( a + ib )( a ib ) = a 2 + iba iab +( ib )( ib )= a 2 + b 2 , which is always real since both a and b are real. (b) | nm | = | ( a + ib )( c + id ) | = | ac + iad + ibc i ) 2 bd | = | ( ac bd )+ i ( ad + bc ) | = p ( ac bd ) 2 ad + bc ) 2 = p a 2 c 2 + b 2 d 2 + a 2 d 2 + b 2 c 2 . But | n || m | = | a + ib c +
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