1. The problem is to find the absolute value (or modulus) of the complex number $2i$. 2. The formula for the absolute value of a complex number $a + bi$ is: $$|a + bi| = \sqrt{a^2 + b^2}$$ where $a$ is the real part and $b$ is the imaginary part. 3. For the complex number $2i$, the real part $a = 0$ and the imaginary part $b = 2$. 4. Substitute these values into the formula: $$|2i| = \sqrt{0^2 + 2^2} = \sqrt{0 + 4} = \sqrt{4}$$ 5. Simplify the square root: $$\sqrt{4} = 2$$ 6. Therefore, the absolute value of $2i$ is $2$.