What are the roots of the equation $$ x^{2}+8 x+65=0 $$ in simplest $$ a+b i $$ form?

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Solve the equation $$ x^{2}+8x+65=0 $$.
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using the quadratic formula in the complex numbers system:
  $$x^{2}+8x+65=0$$
- step1: Solve using the quadratic formula:
  $$x=\frac{-8\pm \sqrt{8^{2}-4	imes 65}}{2}$$
- step2: Simplify the expression:
  $$x=\frac{-8\pm \sqrt{-196}}{2}$$
- step3: Simplify the expression:
  $$x=\frac{-8\pm 14i}{2}$$
- step4: Separate into possible cases:
  $$\begin{align}&x=\frac{-8+14i}{2}\&x=\frac{-8-14i}{2}\end{align}$$
- step5: Simplify the expression:
  $$\begin{align}&x=-4+7i\&x=\frac{-8-14i}{2}\end{align}$$
- step6: Simplify the expression:
  $$\begin{align}&x=-4+7i\&x=-4-7i\end{align}$$
- step7: Rewrite:
  $$x_{1}=-4-7i,x_{2}=-4+7i$$
The roots of the equation $$ x^{2}+8x+65=0 $$ in simplest $$ a+bi $$ form are $$ x_{1}=-4-7i $$ and $$ x_{2}=-4+7i $$.
The roots are $$ x_{1}=-4-7i $$ and $$ x_{2}=-4+7i $$.

What are the roots of the equation in simplest form?

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