Answer: x^2+4
Work Shown:
x = -2i
x^2 = (-2i)^2
x^2 = 4i^2
x^2 = 4(-1)
x^2 = -4
x^2+4 = 0
Side note: Since -2i is one root, this means 2i is the other conjugate root.
[tex]\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0[/tex]
