Question

Va rog ajutati-ma. Am atasat o fotografie cu problema pe care o am. Multumesc anticipat

Answer 1

 

$\displaystyle\bf\\z^2+z-\overline{z}=0\\\\z=a+bi\\\overline{z}=a-bi\\\\z^2+z-\overline{z}=0\\(a+bi)^2+(a+bi)-(a-bi)=0\\\\a^2+2abi+b^2i^2+a+bi-a+bi=0\\\\a^2-b^2+2abi+2bi=0\\\\(a^2-b^2)+(2ab+2b)i=0\\\\Parta~reala=0~~si~~Parta~imaginara=0\\\\a^2-b^2=0\\2ab+2b=0\\\\a^2=b^2~~\implies~~a=\pm b\\2b(a+1)=0~~\implies~~2b=0~~sau~~a+1=0\\\\Cazul~1:\\2b=0\\b=0a=\pmb=0\\a=0\\z_1=0+0i\\\boxed{\bf z_1=0}\\\\Cazul~2:\\a+1=0\\a=-1\\b_1=1~si~b_2=-1\\\\\boxed{\bf z_2=-1+i}\\\boxed{\bf z_3=-1-i}$

Raspuns corect E)