To simplify $i^{49}$, we first note that the powers of the imaginary unit $i$ cycle every four steps:

• $i^1 = i$
• $i^2 = -1$
• $i^3 = -i$
• $i^4 = 1$

This cycle repeats, so $i^5 = i$, $i^6 = -1$, and so forth. To simplify $i^{49}$, we find the remainder of 49 divided by 4:

$49 \div 4 = 12 \text{ remainder } 1.$

So, $i^{49} = i^1 = i$.

Now, let's determine the sets to which this value belongs:

1. Complex Numbers ($\mathbb{C}$): $i$ is a complex number, as it includes all numbers of the form $a + bi$ where $a$ and $b$ are real numbers.
2. Imaginary Numbers: Specifically, $i$ is an imaginary number since it is a multiple of the imaginary unit $i$ and has no real part.

These are the primary sets that $i$ belongs to. It is not a real number, rational number, integer, or natural number.