(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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