Suppose I have a complex number $C = \left | C \right | e^{i\phi}$ where | | denotes modulus and $\phi$ is the phase angle.
Now, I know the error in the modulus, $\delta |C|$ and error in the phase, $\delta\phi$. What are the error propagation rules to determine the overall error, $\delta C$?
Edit: The "error" I'm referring to is 1 standard deviation.