Question

复数问题在复数C中解下列方程组:

Answer 1

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