Uppgift 9

\\z_{1}=1\\z_{2}=-i\\\\detta\;ger\;oss:\\(z-i)(z-(-i))(z^{2}+az+b)=0\\(z-i)(z+i)(z^{2}+az+b)=0\\(z^{2}+1)(z^{2}+az+b)=0\\z^{4}+a\cdot z^{3}+b\cdot z^{2}+z^{2}+az+b=0\\z^{4}+a\cdot z^{3}+(b+1)z^{2}+az+b=0\\\\vi\;j\ddot{a}mf\ddot{o}r\;med\;ursprungsekvationen:\\\\a=-1\\b+1=0\Rightarrow b=-1\\\\ins\ddot{a}ttning\;ger\;oss:\\\\z^{2}-z-1=0z=\frac{1}{2}\pm \sqrt{(\frac{1}{2})^{2}+1}\\\\z=\frac{1}{2}\pm \sqrt{\frac{1}{4}+\frac{4}{4}}\\\\z=\frac{1}{2}\pm \sqrt{\frac{5}{4}}\\\\z_{3}=\frac{1}{2}+\frac{\sqrt{5}}{2}\\\\z_{4}=\frac{1}{2}-\frac{\sqrt{5}}{2}\\