How does this go from x^2+ to 2i, explain.

you want to rephrase that question? Meaningless as it is.

and fyi 2i is an imaginary number...

To go from "x^2+" to "2i," it seems like you're trying to solve a quadratic equation. However, there is missing information that prevents me from providing a clear explanation. In a quadratic equation, the standard form is usually ax^2 + bx + c = 0, where a, b, and c are constants. Additionally, "i" represents the imaginary unit, where i^2 = -1.

If you have an equation like "x^2 + 2i = 0" or "x^2 + 2ix = 0," we can walk through the process:

Step 1: Move all the terms to one side of the equation, so it becomes "x^2 + 2i = 0."
Step 2: Try factoring the equation. However, in this case, it's not possible to factor since there is no real number whose square is -2i.
Step 3: Use the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). However, in this case, there is no b or c term, so "b^2 - 4ac" will be simplified to (-4)(1)(2i) = -8i.
Step 4: Apply the quadratic formula. Since there is no b term, we have x = (0 ± √(-8i)) / (2 * 1).
Step 5: Simplify the square root of -8i. This requires finding the principal square root. In this case, it is 2√2 * √(-i) = 2√2 * (1-i).
Step 6: Continuing from Step 4, we have x = (0 ± 2√2 * (1-i)) / 2, which simplifies to x = ±√2 * (1-i).
Step 7: Express the answer in the form of a complex number. The answer is x = ±√2 - √2i.

Please note that without additional context or a more specific equation, it is challenging to give a complete response.