✐ Answer:
[tex]n^2+n+2=0\quad :\quad n=-\frac{1}{2}+i\frac{\sqrt{7}}{2},\:n=-\frac{1}{2}-i\frac{\sqrt{7}}{2}[/tex]
✍️Steps:--
✰ [tex]n^2+n+2=0[/tex]
[tex]n_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}[/tex]
[tex]n_{1,\:2}=\frac{-1\pm \sqrt{7}i}{2\cdot \:1}[/tex]
[tex]n_1=\frac{-1+\sqrt{7}i}{2\cdot \:1},\:n_2=\frac{-1-\sqrt{7}i}{2\cdot \:1}[/tex]
[tex]\frac{-1+\sqrt{7}i}{2\cdot \:1}[/tex]
[tex]=\frac{-1+\sqrt{7}i}{2}[/tex]
[tex]=-\frac{1}{2}+\frac{\sqrt{7}}{2}[/tex]
[tex]\frac{-1-\sqrt{7}i}{2\cdot \:1}[/tex]
[tex]=\frac{-1-\sqrt{7}i}{2}[/tex]
[tex]=-\frac{1}{2}-\frac{\sqrt{7}}{2}[/tex]
[tex]n=-\frac{1}{2}+i\frac{\sqrt{7}}{2},\:n=-\frac{1}{2}-i\frac{\sqrt{7}}{2}[/tex]
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hope it helps...
have a great day!!
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