[tex]z_{1} \circ z_{2}=z_{1}+z_{2}+z_{1} z_{2}[/tex]
a)
[tex](1+i)\circ (2-i)=1+i+2-i+(1+i)(2-i)=3+2+i-i^2=5+1+i=6+i[/tex]
b)
Fie z=a+bi
[tex]\bar{z}=a-bi[/tex]
[tex]z\circ \bar{z}=(a+bi)\circ (a-bi)=a+bi+a-bi+(a+bi)(a-bi)\\\\z\circ \bar{z}=2a+a^2-bi^2=2a+a^2+b^2\in R[/tex]
c)
[tex]z\circ z=-2\\\\z+z+z^2=-2\\\\z^2+2z+2=0\\\\\Delta=4-8=-4\\\\z_1=\frac{-2+2i}{2} =i-1\\\\z_2=\frac{-2-2i}{2} =-1-i[/tex]
Un alt exercitiu cu legi de compozitie gasesti aici: https://brainly.ro/tema/9905545
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