Since $i$ is the imaginary unit and $i^2 = -1$, we can simplify the given expression as follows:
\begin{align*}
i^{14762} + i^{14763} + i^{14764} + i^{14765} &= (i^2)^{7381} \cdot i + (i^2)^{7381} \cdot i^2 + (i^2)^{7382} \cdot i + (i^2)^{7382} \cdot i^2 \\
&= (-1)^{7381} \cdot i + (-1)^{7381} \cdot (-1) + (-1)^{7382} \cdot i + (-1)^{7382} \cdot (-1) \\
&= -i + 1 + i - 1 \\
&= \boxed{0}.
\end{align*}
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:
