[tex]\displaystyle z=\frac{8-9i}{-5+2i} =\frac{(8-9i)(-5-2i)}{(-5+2i)(-5-2i)}=\\ \\ =\frac{8 \cdot (-5)+8 \cdit (-2i)-9i \cdot (-5)-9i\cdot(-2i)}{(-5)^2+2^2}=\frac{-40-16i+45i+18i^2}{25+4} = \\ \\ =\frac{-40+29i+18 \cdot (-1)}{29} =\frac{-40+29i-18}{29} =\frac{-58+29i}{29} = \\ \\ =\frac{29(-2+i)}{29} =-2+i \\ \\ \mathbf{Re(z)=-2}[/tex]
