Răspuns:
a) (x+2y)+(7x+y)i=3+8i
[tex]\left \{{x+2y=3|*7} \atop {7x+y=8}} \right\\\left \{{7x+14y=21} \atop {7x+y=8}} \right\\13y=13\\y=1\\x+2*1=3\\x=1[/tex]
c)
[tex](x+1)(1-i)+(1-y)(1+i)=4\\x-xi+1-i+1+i-y-yi=4\\x-y+2+i(-x-y)=4\\\left \{{x-y+2=4} \atop {-x-y=0} \right\\\left \{{x-y=2} \atop {-x-y=0} \right\\-2y=2\\y=-1\\-x-(-1)=0\\-x=-1\\x=1[/tex]
d)
[tex](x+y+i)(1+i)=(x+yi-1)(1-i)\\x+xi+y+yi+i+i^2=x+-xi+yi-yi^2-1+i\\x+y+i(x+y+1)-1=x+y+i(-x+y+1)-1\\i(x+y+1)=i(-x+y+1)\\x+y+1=-x+y+1\\2x=0\\x=0\\[/tex]
y∈R
Explicație pas cu pas:
