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(1)求w=(8j)^(1/3)?

w1=[8(cos90°+jsin90°)]^(1/3)

=2(cos30°+jsin30°).....戴美弗定理

=2(√3/2+j/2)

=√3+j

w2=2(cos150°+jsin150°).....30+120=150

=2(-cos30°+jsin30°)

=2(-√3/2+j/2)

=√3-j

w3=2(cos270°+jsin270°).....150+120=270

=2(0-j)

=-2j

(2)將上一小題的三次方根對應到複數平面上的點,並求以這些點為頂點所圍成的

圖形面積?

w1=(√3,1), w2=(√3,-1), w3=(0,-2)

A=|.0 √3 -√3 0|
..|-2 .1 .-1 .-2|/2

=(-√3+2√3+2√3+√3)/2

=2√3

(3)求u=[8(-1+√3j)]^(1/4)

u1=[16(-1/2+j√3/2)]^(1/4)

=2(cos120°+jsin120°)^(1/4).....戴美弗定理

=2(cos30°+jsin30°)

=2(√3/2+j/2)

=√3+j

u2=2(cos120°+jsin120°).....30+90=120

=2(-1/2+j√3/2)

=-1+j√3

u3=2(cos210°+jsin210°).....120+90=210

=2(-√3/2-j/2)

=-√3-j

u4=2(cos300°+jsin300°).....210+90=300

=2(1/2-j√3/2)°°°°°°°°°°°

=1-j√3

(4)將上一小題的4次方根對應到複數平面上的點,並求以這些點為頂點所圍成的圖

形面積?

u1=(√3,1), u2=(-1,√3), u3=(-√3,-1), u4=(1,-√3)

A=|√3 -1 -√3. 1 .√3|
..|.1 √3 -1 .-√3 .1.|/2

=(3+1+3+1+1+3+1+3)/2

=(12+4)/2

=8

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