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a=(1+√3j)/2

=1/2+j√3/2

=cos(60)+jsin(60)

a^20=[cos60+jsin(60)]^20

=cos(1200)+jsin(1200).....戴美弗定理

=cos(3*360+120)+jsin(3*360+120)

=cos120+jsin120

=-1/2+j√3/2

b=a-1

=-1/2+j√3/2

=cos(120)+jsin(120)

b^10=cos1200+jsin1200

=cos(3*360+120)+jsin(3*360+120)

=cos120+jsin120

=-1/2+j√3/2

c=a-j√3

=1/2-j√3/2

=cos(300)+jsin(300)

c^30=cos(9000)+jsin(9000)

=cos(25*360)+jsin(25*360)

=cos0+jsin0

=1

代入上式:

w=|a^20*b^10/5*c^30|

=|(-1/2+j√3/2)^2/(5*1)|

=|(1/4-3/4-j√3/2)/5|

=|-(1/2+j√3/2)/5|

=|(1+j√3)/10|

=√(1+3)/10

=2/10

=1/5

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