We know that $i^2 = -1$, so $i^4 = (-1)^2 = 1$.
Since $i^4 = 1$, we can reduce the exponents modulo 4.
We have $14762 \equiv 2 \pmod{4}$, $14763 \equiv 3 \pmod{4}$, $14764 \equiv 0 \pmod{4}$, and $14765 \equiv 1 \pmod{4}$.
Therefore, $i^{14762} = i^2 = -1$, $i^{14763} = i^3 = -i$, $i^{14764} = i^0 = 1$, and $i^{14765} = i^1 = i$.
Thus, $i^{14762} + i^{14763} + i^{14764} + i^{14765} = -1 - i + 1 + i = \boxed{0}$.
The answer is: 0
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of $i^{14762} + i^{14763} + i^{14764} + i^{14765}$?

### Answer:
