Angle units in complex planes

Question

$$ z = re^{i\theta} $$

I have seen that, when specifying a complex number, most people would rather use radians as the units for $\theta.$ Is it incorrect to use degrees? Why is there a preference for radians?

Answer 1

You can use degrees… However, if you do so, then for a flat angle of $180°$ you don’t have the famous relation $$e^{i\pi}=-1$$ which holds if you use radians.