Solve the equation in the complex number syste $$ x^{2}+36=0 $$

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1. Start with the equation:
   $$
   x^2 + 36 = 0
   $$

2. Subtract $$36$$ from both sides to isolate $$x^2$$:
   $$
   x^2 = -36
   $$

3. Take the square root of both sides. Recall that the square root of a negative number introduces the imaginary unit $$i$$, where $$i^2 = -1$$:
   $$
   x = \pm \sqrt{-36} = \pm \sqrt{36} \cdot \sqrt{-1} = \pm 6i
   $$

4. The solutions to the equation are:
   $$
   x = 6i \quad \text{and} \quad x = -6i
   $$
The solutions are $$ x = 6i $$ and $$ x = -6i $$.

Solve the equation in the complex number syste

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