复数问题在复数C中解下列方程组:

题目

复数问题在复数C中解下列方程组:
1) x+iy-2z=10
x-y+2iz=20
ix+3iy-(1+i)z=30
2) x^2+y^2=6
y^2+z^2=0
z^2+x^2=8i
3) x^2+y^2-2xy+3(x+y)-2=0
2(x^2+y^2)-2xy-2(x+y)+15=0
4) (x-y)/(1+xy)=1/3
(x+y)/(1-xy)=3
5) x+y+z=13
x^2+y^2+z^2=65
yz=10

答案

1) x+iy-2z=10
x-y+2iz=20
ix+3iy-(1+i)z=30
z=1-7i,x=3-11i,y=-3-9i
2) x^2+y^2=6
y^2+z^2=0
z^2+x^2=8i
z=±(1+2i),x=±(2+i),y=±(2-i)
3) x^2+y^2-2xy+3(x+y)-2=0
2(x^2+y^2)-2xy-2(x+y)+15=0
x=9/2-5i/2 y=9/2+5i/2
x=9/2+5i/2 y=9/2-5i/2
x=2-i*sqrt(10)/2 y=2+i*sqrt(10)/2
x=2+i*sqrt(10)/2 y=2-i*sqrt(10)/2
4) (x-y)/(1+xy)=1/3
(x+y)/(1-xy)=3
x=-1 y=-2
x=1 y=1/2
5) x+y+z=13
x^2+y^2+z^2=65
yz=10
z=5 x=6 y=2
z=2 x=6 y=5
z=3+i x=7 y=3-i
z=3-1 x=7 y=3+1